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data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Top)</div> </a> </li> <li id="toc-Introduction" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Introduction"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Introduction</span> </div> </a> <ul id="toc-Introduction-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Examples" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Examples"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Examples</span> </div> </a> <ul id="toc-Examples-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Applications" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Applications"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Applications</span> </div> </a> <button aria-controls="toc-Applications-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Applications subsection</span> </button> <ul id="toc-Applications-sublist" class="vector-toc-list"> <li id="toc-Lubrication" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Lubrication"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Lubrication</span> </div> </a> <ul id="toc-Lubrication-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Solvation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Solvation"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Solvation</span> </div> </a> <ul id="toc-Solvation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cooling" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Cooling"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Cooling</span> </div> </a> <ul id="toc-Cooling-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cooking" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Cooking"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Cooking</span> </div> </a> <ul id="toc-Cooking-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Distillation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Distillation"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5</span> <span>Distillation</span> </div> </a> <ul id="toc-Distillation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Hydraulics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Hydraulics"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.6</span> <span>Hydraulics</span> </div> </a> <ul id="toc-Hydraulics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Liquid_metals" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Liquid_metals"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.7</span> <span>Liquid metals</span> </div> </a> <ul id="toc-Liquid_metals-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Miscellaneous" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Miscellaneous"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.8</span> <span>Miscellaneous</span> </div> </a> <ul id="toc-Miscellaneous-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Mechanical_properties" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Mechanical_properties"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Mechanical properties</span> </div> </a> <button aria-controls="toc-Mechanical_properties-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Mechanical properties subsection</span> </button> <ul id="toc-Mechanical_properties-sublist" class="vector-toc-list"> <li id="toc-Volume" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Volume"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Volume</span> </div> </a> <ul id="toc-Volume-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pressure_and_buoyancy" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Pressure_and_buoyancy"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Pressure and buoyancy</span> </div> </a> <ul id="toc-Pressure_and_buoyancy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Surfaces" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Surfaces"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Surfaces</span> </div> </a> <ul id="toc-Surfaces-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Flow" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Flow"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Flow</span> </div> </a> <ul id="toc-Flow-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sound_propagation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sound_propagation"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.5</span> <span>Sound propagation</span> </div> </a> <ul id="toc-Sound_propagation-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Thermodynamics" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Thermodynamics"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Thermodynamics</span> </div> </a> <button aria-controls="toc-Thermodynamics-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Thermodynamics subsection</span> </button> <ul id="toc-Thermodynamics-sublist" class="vector-toc-list"> <li id="toc-Phase_transitions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Phase_transitions"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Phase transitions</span> </div> </a> <ul id="toc-Phase_transitions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Liquids_in_space" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Liquids_in_space"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Liquids in space</span> </div> </a> <ul id="toc-Liquids_in_space-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Solutions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Solutions"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Solutions</span> </div> </a> <ul id="toc-Solutions-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Microscopic_description" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Microscopic_description"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Microscopic description</span> </div> </a> <button aria-controls="toc-Microscopic_description-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Microscopic description subsection</span> </button> <ul id="toc-Microscopic_description-sublist" class="vector-toc-list"> <li id="toc-General_description" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#General_description"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>General description</span> </div> </a> <ul id="toc-General_description-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Short-range_ordering" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Short-range_ordering"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Short-range ordering</span> </div> </a> <ul id="toc-Short-range_ordering-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Energy_and_entropy" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Energy_and_entropy"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3</span> <span>Energy and entropy</span> </div> </a> <ul id="toc-Energy_and_entropy-sublist" class="vector-toc-list"> <li id="toc-No_small_parameter" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#No_small_parameter"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3.1</span> <span>No small parameter</span> </div> </a> <ul id="toc-No_small_parameter-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Role_of_quantum_mechanics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Role_of_quantum_mechanics"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.4</span> <span>Role of quantum mechanics</span> </div> </a> <ul id="toc-Role_of_quantum_mechanics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dynamic_phenomena" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Dynamic_phenomena"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.5</span> <span>Dynamic phenomena</span> </div> </a> <ul id="toc-Dynamic_phenomena-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Experimental_methods" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Experimental_methods"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.6</span> <span>Experimental methods</span> </div> </a> <ul id="toc-Experimental_methods-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Prediction_of_liquid_properties" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Prediction_of_liquid_properties"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Prediction of liquid properties</span> </div> </a> <button aria-controls="toc-Prediction_of_liquid_properties-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Prediction of liquid properties subsection</span> </button> <ul id="toc-Prediction_of_liquid_properties-sublist" class="vector-toc-list"> <li id="toc-Macroscopic" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Macroscopic"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Macroscopic</span> </div> </a> <ul id="toc-Macroscopic-sublist" class="vector-toc-list"> <li id="toc-Empirical_correlations" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Empirical_correlations"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1.1</span> <span>Empirical correlations</span> </div> </a> <ul id="toc-Empirical_correlations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Thermodynamic_potentials" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Thermodynamic_potentials"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1.2</span> <span>Thermodynamic potentials</span> </div> </a> <ul id="toc-Thermodynamic_potentials-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Hydrodynamics" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Hydrodynamics"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1.3</span> <span>Hydrodynamics</span> </div> </a> <ul id="toc-Hydrodynamics-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Mesoscopic" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mesoscopic"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>Mesoscopic</span> </div> </a> <ul id="toc-Mesoscopic-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Microscopic" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Microscopic"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.3</span> <span>Microscopic</span> </div> </a> <ul id="toc-Microscopic-sublist" class="vector-toc-list"> <li id="toc-Classical_molecular_dynamics" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Classical_molecular_dynamics"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.3.1</span> <span>Classical molecular dynamics</span> </div> </a> <ul id="toc-Classical_molecular_dynamics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ab_initio_(quantum)_molecular_dynamics" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Ab_initio_(quantum)_molecular_dynamics"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.3.2</span> <span>Ab initio (quantum) molecular dynamics</span> </div> </a> <ul id="toc-Ab_initio_(quantum)_molecular_dynamics-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Liquid</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 133 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-133" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">133 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Vloeistof" title="Vloeistof – Afrikaans" lang="af" hreflang="af" data-title="Vloeistof" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Fl%C3%BCssigkeit" title="Flüssigkeit – Alemannic" lang="gsw" hreflang="gsw" data-title="Flüssigkeit" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-anp mw-list-item"><a href="https://anp.wikipedia.org/wiki/%E0%A4%A6%E0%A5%8D%E0%A4%B0%E0%A4%B5" title="द्रव – Angika" lang="anp" hreflang="anp" data-title="द्रव" data-language-autonym="अंगिका" data-language-local-name="Angika" class="interlanguage-link-target"><span>अंगिका</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B3%D8%A7%D8%A6%D9%84" title="سائل – Arabic" lang="ar" hreflang="ar" data-title="سائل" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Liquido" title="Liquido – Aragonese" lang="an" hreflang="an" data-title="Liquido" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%A4%E0%A7%B0%E0%A6%B2_%E0%A6%AA%E0%A6%A6%E0%A6%BE%E0%A7%B0%E0%A7%8D%E0%A6%A5" title="তৰল পদাৰ্থ – Assamese" lang="as" hreflang="as" data-title="তৰল পদাৰ্থ" data-language-autonym="অসমীয়া" data-language-local-name="Assamese" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/L%C3%ADquidu" title="Líquidu – Asturian" lang="ast" hreflang="ast" data-title="Líquidu" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Maye" title="Maye – Azerbaijani" lang="az" hreflang="az" data-title="Maye" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D9%85%D8%A7%DB%8C%D8%B9" title="مایع – South Azerbaijani" lang="azb" hreflang="azb" data-title="مایع" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%A4%E0%A6%B0%E0%A6%B2" title="তরল – Bangla" lang="bn" hreflang="bn" data-title="তরল" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/E%CC%8Dk-th%C3%A9" title="E̍k-thé – Minnan" lang="nan" hreflang="nan" data-title="E̍k-thé" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%A8%D1%8B%D0%B9%D1%8B%D2%A1%D1%81%D0%B0" title="Шыйыҡса – Bashkir" lang="ba" hreflang="ba" data-title="Шыйыҡса" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%92%D0%B0%D0%B4%D0%BA%D0%B0%D1%81%D1%86%D1%8C" title="Вадкасць – Belarusian" lang="be" hreflang="be" data-title="Вадкасць" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%92%D0%B0%D0%B4%D0%BA%D0%B0%D1%81%D1%8C%D1%86%D1%8C" title="Вадкасьць – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Вадкасьць" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Likido" title="Likido – Central Bikol" lang="bcl" hreflang="bcl" data-title="Likido" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A2%D0%B5%D1%87%D0%BD%D0%BE%D1%81%D1%82" title="Течност – Bulgarian" lang="bg" hreflang="bg" data-title="Течност" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Te%C4%8Dnost" title="Tečnost – Bosnian" lang="bs" hreflang="bs" data-title="Tečnost" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-bxr mw-list-item"><a href="https://bxr.wikipedia.org/wiki/%D0%A8%D1%8D%D0%BD%D0%B3%D1%8D%D0%BD" title="Шэнгэн – Russia Buriat" lang="bxr" hreflang="bxr" data-title="Шэнгэн" data-language-autonym="Буряад" data-language-local-name="Russia Buriat" class="interlanguage-link-target"><span>Буряад</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/L%C3%ADquid" title="Líquid – Catalan" lang="ca" hreflang="ca" data-title="Líquid" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A8%C4%95%D0%B2%D0%B5%D0%BA" title="Шĕвек – Chuvash" lang="cv" hreflang="cv" data-title="Шĕвек" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-ceb mw-list-item"><a href="https://ceb.wikipedia.org/wiki/Likido" title="Likido – Cebuano" lang="ceb" hreflang="ceb" data-title="Likido" data-language-autonym="Cebuano" data-language-local-name="Cebuano" class="interlanguage-link-target"><span>Cebuano</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Kapalina" title="Kapalina – Czech" lang="cs" hreflang="cs" data-title="Kapalina" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Mutuvi" title="Mutuvi – Shona" lang="sn" hreflang="sn" data-title="Mutuvi" data-language-autonym="ChiShona" data-language-local-name="Shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Hylif" title="Hylif – Welsh" lang="cy" hreflang="cy" data-title="Hylif" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/V%C3%A6ske" title="Væske – Danish" lang="da" hreflang="da" data-title="Væske" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D8%B3%D8%A7%D9%8A%D9%84" title="سايل – Moroccan Arabic" lang="ary" hreflang="ary" data-title="سايل" data-language-autonym="الدارجة" data-language-local-name="Moroccan Arabic" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Fl%C3%BCssigkeit" title="Flüssigkeit – German" lang="de" hreflang="de" data-title="Flüssigkeit" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Vedelik" title="Vedelik – Estonian" lang="et" hreflang="et" data-title="Vedelik" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A5%CE%B3%CF%81%CF%8C" title="Υγρό – Greek" lang="el" hreflang="el" data-title="Υγρό" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/L%C3%ADquido" title="Líquido – Spanish" lang="es" hreflang="es" data-title="Líquido" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Likvo" title="Likvo – Esperanto" lang="eo" hreflang="eo" data-title="Likvo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Likido" title="Likido – Basque" lang="eu" hreflang="eu" data-title="Likido" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%A7%DB%8C%D8%B9" title="مایع – Persian" lang="fa" hreflang="fa" data-title="مایع" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Liquid" title="Liquid – Fiji Hindi" lang="hif" hreflang="hif" data-title="Liquid" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji Hindi" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Liquide" title="Liquide – French" lang="fr" hreflang="fr" data-title="Liquide" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Leacht" title="Leacht – Irish" lang="ga" hreflang="ga" data-title="Leacht" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gv mw-list-item"><a href="https://gv.wikipedia.org/wiki/Ushlaght" title="Ushlaght – Manx" lang="gv" hreflang="gv" data-title="Ushlaght" data-language-autonym="Gaelg" data-language-local-name="Manx" class="interlanguage-link-target"><span>Gaelg</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/L%C3%ADquido" title="Líquido – Galician" lang="gl" hreflang="gl" data-title="Líquido" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%AA%E0%AB%8D%E0%AA%B0%E0%AA%B5%E0%AA%BE%E0%AA%B9%E0%AB%80" title="પ્રવાહી – Gujarati" lang="gu" hreflang="gu" data-title="પ્રવાહી" data-language-autonym="ગુજરાતી" data-language-local-name="Gujarati" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-hak mw-list-item"><a href="https://hak.wikipedia.org/wiki/Yi%CC%8Dt-th%C3%AD" title="Yi̍t-thí – Hakka Chinese" lang="hak" hreflang="hak" data-title="Yi̍t-thí" data-language-autonym="客家語 / Hak-kâ-ngî" data-language-local-name="Hakka Chinese" class="interlanguage-link-target"><span>客家語 / Hak-kâ-ngî</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%95%A1%EC%B2%B4" title="액체 – Korean" lang="ko" hreflang="ko" data-title="액체" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%80%D5%A5%D5%B2%D5%B8%D6%82%D5%AF" title="Հեղուկ – Armenian" lang="hy" hreflang="hy" data-title="Հեղուկ" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%A6%E0%A5%8D%E0%A4%B0%E0%A4%B5" title="द्रव – Hindi" lang="hi" hreflang="hi" data-title="द्रव" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Teku%C4%87ine" title="Tekućine – Croatian" lang="hr" hreflang="hr" data-title="Tekućine" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Liquido" title="Liquido – Ido" lang="io" hreflang="io" data-title="Liquido" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Cairan" title="Cairan – Indonesian" lang="id" hreflang="id" data-title="Cairan" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Liquido" title="Liquido – Interlingua" lang="ia" hreflang="ia" data-title="Liquido" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-ie mw-list-item"><a href="https://ie.wikipedia.org/wiki/Liquide" title="Liquide – Interlingue" lang="ie" hreflang="ie" data-title="Liquide" data-language-autonym="Interlingue" data-language-local-name="Interlingue" class="interlanguage-link-target"><span>Interlingue</span></a></li><li class="interlanguage-link interwiki-zu mw-list-item"><a href="https://zu.wikipedia.org/wiki/Uketshezi" title="Uketshezi – Zulu" lang="zu" hreflang="zu" data-title="Uketshezi" data-language-autonym="IsiZulu" data-language-local-name="Zulu" class="interlanguage-link-target"><span>IsiZulu</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/V%C3%B6kvi" title="Vökvi – Icelandic" lang="is" hreflang="is" data-title="Vökvi" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Liquido" title="Liquido – Italian" lang="it" hreflang="it" data-title="Liquido" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A0%D7%95%D7%96%D7%9C" title="נוזל – Hebrew" lang="he" hreflang="he" data-title="נוזל" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%A6%E0%B3%8D%E0%B2%B0%E0%B2%B5" title="ದ್ರವ – Kannada" lang="kn" hreflang="kn" data-title="ದ್ರವ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A1%E1%83%98%E1%83%97%E1%83%AE%E1%83%94" title="სითხე – Georgian" lang="ka" hreflang="ka" data-title="სითხე" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A1%D2%B1%D0%B9%D1%8B%D2%9B%D1%82%D1%8B%D2%9B" title="Сұйықтық – Kazakh" lang="kk" hreflang="kk" data-title="Сұйықтық" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Kiowevu" title="Kiowevu – Swahili" lang="sw" hreflang="sw" data-title="Kiowevu" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Likid" title="Likid – Haitian Creole" lang="ht" hreflang="ht" data-title="Likid" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/%C5%9Eile" title="Şile – Kurdish" lang="ku" hreflang="ku" data-title="Şile" data-language-autonym="Kurdî" data-language-local-name="Kurdish" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%A1%D1%83%D1%8E%D0%BA%D1%82%D1%83%D0%BA" title="Суюктук – Kyrgyz" lang="ky" hreflang="ky" data-title="Суюктук" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Liquidum" title="Liquidum – Latin" lang="la" hreflang="la" data-title="Liquidum" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/%C5%A0%C4%B7idrums" title="Šķidrums – Latvian" lang="lv" hreflang="lv" data-title="Šķidrums" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Skystis" title="Skystis – Lithuanian" lang="lt" hreflang="lt" data-title="Skystis" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Vleujstof" title="Vleujstof – Limburgish" lang="li" hreflang="li" data-title="Vleujstof" data-language-autonym="Limburgs" data-language-local-name="Limburgish" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-ln mw-list-item"><a href="https://ln.wikipedia.org/wiki/Bom%C3%A1i" title="Bomái – Lingala" lang="ln" hreflang="ln" data-title="Bomái" data-language-autonym="Lingála" data-language-local-name="Lingala" class="interlanguage-link-target"><span>Lingála</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Liquid" title="Liquid – Lombard" lang="lmo" hreflang="lmo" data-title="Liquid" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Folyad%C3%A9k" title="Folyadék – Hungarian" lang="hu" hreflang="hu" data-title="Folyadék" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A2%D0%B5%D1%87%D0%BD%D0%BE%D1%81%D1%82" title="Течност – Macedonian" lang="mk" hreflang="mk" data-title="Течност" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Ranoka" title="Ranoka – Malagasy" lang="mg" hreflang="mg" data-title="Ranoka" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%A6%E0%B5%8D%E0%B4%B0%E0%B4%BE%E0%B4%B5%E0%B4%95%E0%B4%82" title="ദ്രാവകം – Malayalam" lang="ml" hreflang="ml" data-title="ദ്രാവകം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%A6%E0%A5%8D%E0%A4%B0%E0%A4%B5" title="द्रव – Marathi" lang="mr" hreflang="mr" data-title="द्रव" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%B3%D8%A7%D9%8A%D9%84" title="سايل – Egyptian Arabic" lang="arz" hreflang="arz" data-title="سايل" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Cecair" title="Cecair – Malay" lang="ms" hreflang="ms" data-title="Cecair" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-cdo mw-list-item"><a href="https://cdo.wikipedia.org/wiki/%C4%ACk-t%C4%81%CC%A4" title="Ĭk-tā̤ – Mindong" lang="cdo" hreflang="cdo" data-title="Ĭk-tā̤" data-language-autonym="閩東語 / Mìng-dĕ̤ng-ngṳ̄" data-language-local-name="Mindong" class="interlanguage-link-target"><span>閩東語 / Mìng-dĕ̤ng-ngṳ̄</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A8%D0%B8%D0%BD%D0%B3%D1%8D%D0%BD" title="Шингэн – Mongolian" lang="mn" hreflang="mn" data-title="Шингэн" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A1%E1%80%9B%E1%80%8A%E1%80%BA" title="အရည် – Burmese" lang="my" hreflang="my" data-title="အရည်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Waini" title="Waini – Fijian" lang="fj" hreflang="fj" data-title="Waini" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="Fijian" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Vloeistof" title="Vloeistof – Dutch" lang="nl" hreflang="nl" data-title="Vloeistof" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%A4%E0%A4%B0%E0%A4%B2" title="तरल – Nepali" lang="ne" hreflang="ne" data-title="तरल" data-language-autonym="नेपाली" data-language-local-name="Nepali" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%A4%E0%A4%BF" title="ति – Newari" lang="new" hreflang="new" data-title="ति" data-language-autonym="नेपाल भाषा" data-language-local-name="Newari" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%B6%B2%E4%BD%93" title="液体 – Japanese" lang="ja" hreflang="ja" data-title="液体" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/W%C3%A4%C3%A4sk" title="Wääsk – Northern Frisian" lang="frr" hreflang="frr" data-title="Wääsk" data-language-autonym="Nordfriisk" data-language-local-name="Northern Frisian" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/V%C3%A6ske" title="Væske – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Væske" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/V%C3%A6ske" title="Væske – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Væske" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-nov mw-list-item"><a href="https://nov.wikipedia.org/wiki/Liquide" title="Liquide – Novial" lang="nov" hreflang="nov" data-title="Liquide" data-language-autonym="Novial" data-language-local-name="Novial" class="interlanguage-link-target"><span>Novial</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Liquid" title="Liquid – Occitan" lang="oc" hreflang="oc" data-title="Liquid" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Dhangala%27oo" title="Dhangala'oo – Oromo" lang="om" hreflang="om" data-title="Dhangala'oo" data-language-autonym="Oromoo" data-language-local-name="Oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Suyuqlik" title="Suyuqlik – Uzbek" lang="uz" hreflang="uz" data-title="Suyuqlik" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%A4%E0%A8%B0%E0%A8%B2" title="ਤਰਲ – Punjabi" lang="pa" hreflang="pa" data-title="ਤਰਲ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D9%85%D8%A7%D8%A6%D8%B9" title="مائع – Western Punjabi" lang="pnb" hreflang="pnb" data-title="مائع" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D9%85%D8%A7%D9%8A%D8%B9" title="مايع – Pashto" lang="ps" hreflang="ps" data-title="مايع" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Fletigkeit" title="Fletigkeit – Low German" lang="nds" hreflang="nds" data-title="Fletigkeit" data-language-autonym="Plattdüütsch" data-language-local-name="Low German" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Ciecz" title="Ciecz – Polish" lang="pl" hreflang="pl" data-title="Ciecz" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/L%C3%ADquido" title="Líquido – Portuguese" lang="pt" hreflang="pt" data-title="Líquido" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Lichid" title="Lichid – Romanian" lang="ro" hreflang="ro" data-title="Lichid" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Puriqlla" title="Puriqlla – Quechua" lang="qu" hreflang="qu" data-title="Puriqlla" data-language-autonym="Runa Simi" data-language-local-name="Quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%96%D0%B8%D0%B4%D0%BA%D0%BE%D1%81%D1%82%D1%8C" title="Жидкость – Russian" lang="ru" hreflang="ru" data-title="Жидкость" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/L%C3%ABngu" title="Lëngu – Albanian" lang="sq" hreflang="sq" data-title="Lëngu" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Statu_liquitu" title="Statu liquitu – Sicilian" lang="scn" hreflang="scn" data-title="Statu liquitu" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%AF%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B7%80" title="ද්‍රව – Sinhala" lang="si" hreflang="si" data-title="ද්‍රව" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Liquid" title="Liquid – Simple English" lang="en-simple" hreflang="en-simple" data-title="Liquid" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D9%85%D8%A7%D9%8A%D8%B9" title="مايع – Sindhi" lang="sd" hreflang="sd" data-title="مايع" data-language-autonym="سنڌي" data-language-local-name="Sindhi" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Kvapalina" title="Kvapalina – Slovak" lang="sk" hreflang="sk" data-title="Kvapalina" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Kapljevina" title="Kapljevina – Slovenian" lang="sl" hreflang="sl" data-title="Kapljevina" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Dareere" title="Dareere – Somali" lang="so" hreflang="so" data-title="Dareere" data-language-autonym="Soomaaliga" data-language-local-name="Somali" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%B4%D9%84%DB%95" title="شلە – Central Kurdish" lang="ckb" hreflang="ckb" data-title="شلە" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A2%D0%B5%D1%87%D0%BD%D0%BE%D1%81%D1%82" title="Течност – Serbian" lang="sr" hreflang="sr" data-title="Течност" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Te%C4%8Dno_agregatno_stanje" title="Tečno agregatno stanje – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Tečno agregatno stanje" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Cacai" title="Cacai – Sundanese" lang="su" hreflang="su" data-title="Cacai" data-language-autonym="Sunda" data-language-local-name="Sundanese" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Neste" title="Neste – Finnish" lang="fi" hreflang="fi" data-title="Neste" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/V%C3%A4tska" title="Vätska – Swedish" lang="sv" hreflang="sv" data-title="Vätska" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Likido" title="Likido – Tagalog" lang="tl" hreflang="tl" data-title="Likido" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A8%E0%AF%80%E0%AE%B0%E0%AF%8D%E0%AE%AE%E0%AE%AE%E0%AF%8D" title="நீர்மம் – Tamil" lang="ta" hreflang="ta" data-title="நீர்மம்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Amazzal" title="Amazzal – Kabyle" lang="kab" hreflang="kab" data-title="Amazzal" data-language-autonym="Taqbaylit" data-language-local-name="Kabyle" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/S%C4%B1y%C4%B1ql%C4%B1q" title="Sıyıqlıq – Tatar" lang="tt" hreflang="tt" data-title="Sıyıqlıq" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%A6%E0%B1%8D%E0%B0%B0%E0%B0%B5%E0%B0%82" title="ద్రవం – Telugu" lang="te" hreflang="te" data-title="ద్రవం" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%82%E0%B8%AD%E0%B8%87%E0%B9%80%E0%B8%AB%E0%B8%A5%E0%B8%A7" title="ของเหลว – Thai" lang="th" hreflang="th" data-title="ของเหลว" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B5%D1%8A" title="Моеъ – Tajik" lang="tg" hreflang="tg" data-title="Моеъ" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/S%C4%B1v%C4%B1" title="Sıvı – Turkish" lang="tr" hreflang="tr" data-title="Sıvı" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A0%D1%96%D0%B4%D0%B8%D0%BD%D0%B0" title="Рідина – Ukrainian" lang="uk" hreflang="uk" data-title="Рідина" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%85%D8%A7%D8%A6%D8%B9" title="مائع – Urdu" lang="ur" hreflang="ur" data-title="مائع" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/L%C3%ACcuido" title="Lìcuido – Venetian" lang="vec" hreflang="vec" data-title="Lìcuido" data-language-autonym="Vèneto" data-language-local-name="Venetian" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Nozoluz" title="Nozoluz – Veps" lang="vep" hreflang="vep" data-title="Nozoluz" data-language-autonym="Vepsän kel’" data-language-local-name="Veps" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Ch%E1%BA%A5t_l%E1%BB%8Fng" title="Chất lỏng – Vietnamese" lang="vi" hreflang="vi" data-title="Chất lỏng" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Vedel%C3%BCs" title="Vedelüs – Võro" lang="vro" hreflang="vro" data-title="Vedelüs" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E6%B6%B2%E9%AB%94" title="液體 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="液體" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-vls mw-list-item"><a href="https://vls.wikipedia.org/wiki/Vloeistoffe" title="Vloeistoffe – West Flemish" lang="vls" hreflang="vls" data-title="Vloeistoffe" data-language-autonym="West-Vlams" data-language-local-name="West Flemish" class="interlanguage-link-target"><span>West-Vlams</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Likido" title="Likido – Waray" lang="war" hreflang="war" data-title="Likido" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wo mw-list-item"><a href="https://wo.wikipedia.org/wiki/Yolaakon" title="Yolaakon – Wolof" lang="wo" hreflang="wo" data-title="Yolaakon" data-language-autonym="Wolof" data-language-local-name="Wolof" class="interlanguage-link-target"><span>Wolof</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%B6%B2%E4%BD%93" title="液体 – Wu" lang="wuu" hreflang="wuu" data-title="液体" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A4%D7%9C%D7%99%D7%A1%D7%99%D7%A7%D7%99%D7%99%D7%98" title="פליסיקייט – Yiddish" lang="yi" hreflang="yi" data-title="פליסיקייט" data-language-autonym="ייִדיש" data-language-local-name="Yiddish" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%B6%B2%E9%AB%94" title="液體 – Cantonese" lang="yue" hreflang="yue" data-title="液體" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Sk%C4%ABstis" title="Skīstis – Samogitian" lang="sgs" hreflang="sgs" data-title="Skīstis" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%B6%B2%E4%BD%93" title="液体 – Chinese" lang="zh" hreflang="zh" data-title="液体" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q11435#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li 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see <a href="/wiki/Liquid_(disambiguation)" class="mw-disambig" title="Liquid (disambiguation)">Liquid (disambiguation)</a>.</div> <p class="mw-empty-elt"> </p> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Water_drop_001.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Water_drop_001.jpg/300px-Water_drop_001.jpg" decoding="async" width="300" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Water_drop_001.jpg/450px-Water_drop_001.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Water_drop_001.jpg/600px-Water_drop_001.jpg 2x" data-file-width="3714" data-file-height="2475" /></a><figcaption>The formation of a spherical <a href="/wiki/Drop_(liquid)" title="Drop (liquid)">droplet</a> of liquid <a href="/wiki/Water" title="Water">water</a> minimizes the <a href="/wiki/Surface_area" title="Surface area">surface area</a>, which is the natural result of <a 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3.3em}@media(max-width:640px){body.mediawiki .mw-parser-output .sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}body.skin--responsive .mw-parser-output .sidebar a>img{max-width:none!important}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><table class="sidebar sidebar-collapse nomobile nowraplinks plainlist"><tbody><tr><td class="sidebar-pretitle">Part of a series on</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="/wiki/Continuum_mechanics" title="Continuum mechanics">Continuum mechanics</a></th></tr><tr><td class="sidebar-image"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle J=-D{\frac {d\varphi }{dx}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>J</mi> <mo>=</mo> <mo>−</mo> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>φ</mi> </mrow> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J=-D{\frac {d\varphi }{dx}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1856f88def2056f28ed27c7d31180a6240820ea6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:11.874ex; height:5.509ex;" alt="{\displaystyle J=-D{\frac {d\varphi }{dx}}}"></span><div class="sidebar-caption"><a href="/wiki/Fick%27s_laws_of_diffusion" title="Fick's laws of diffusion">Fick's laws of diffusion</a></div></td></tr><tr><td class="sidebar-content-with-subgroup"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)">Laws</div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar-subgroup"><tbody><tr><th class="sidebar-heading" style="font-style:italic;font-weight:normal;"> Conservations</th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Conservation_of_mass" title="Conservation of mass">Mass</a></li> <li><a href="/wiki/Conservation_of_momentum" class="mw-redirect" title="Conservation of momentum">Momentum</a></li> <li><a href="/wiki/Conservation_of_energy" title="Conservation of energy">Energy</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;font-weight:normal;"> Inequalities</th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Clausius%E2%80%93Duhem_inequality" title="Clausius–Duhem inequality">Clausius–Duhem (entropy)</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Solid_mechanics" title="Solid mechanics">Solid mechanics</a></div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Deformation_(physics)" title="Deformation (physics)">Deformation</a></li> <li><a href="/wiki/Elasticity_(physics)" title="Elasticity (physics)">Elasticity</a> <ul><li><a href="/wiki/Linear_elasticity" title="Linear elasticity">linear</a></li></ul></li> <li><a href="/wiki/Plasticity_(physics)" title="Plasticity (physics)">Plasticity</a></li> <li><a href="/wiki/Hooke%27s_law" title="Hooke's law">Hooke's law</a></li> <li><a href="/wiki/Stress_(mechanics)" title="Stress (mechanics)">Stress</a></li> <li><a href="/wiki/Strain_(mechanics)" title="Strain (mechanics)">Strain</a> <ul><li><a href="/wiki/Finite_strain_theory" title="Finite strain theory">Finite strain</a></li> <li><a href="/wiki/Infinitesimal_strain_theory" title="Infinitesimal strain theory">Infinitesimal strain</a></li></ul></li> <li><a href="/wiki/Compatibility_(mechanics)" title="Compatibility (mechanics)">Compatibility</a></li> <li><a href="/wiki/Bending" title="Bending">Bending</a></li> <li><a href="/wiki/Contact_mechanics" title="Contact mechanics">Contact mechanics</a> <ul><li><a href="/wiki/Frictional_contact_mechanics" title="Frictional contact mechanics">frictional</a></li></ul></li> <li><a href="/wiki/Material_failure_theory" title="Material failure theory">Material failure theory</a></li> <li><a href="/wiki/Fracture_mechanics" title="Fracture mechanics">Fracture mechanics</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content-with-subgroup"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Fluid_mechanics" title="Fluid mechanics">Fluid mechanics</a></div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar-subgroup"><tbody><tr><th class="sidebar-heading" style="font-style:italic;"> <a href="/wiki/Fluid" title="Fluid">Fluids</a></th></tr><tr><td class="sidebar-content"> <div class="wraplinks"> <ul><li><a href="/wiki/Hydrostatics" title="Hydrostatics">Statics</a> <b>·</b> <a href="/wiki/Fluid_dynamics" title="Fluid dynamics">Dynamics</a></li> <li><a href="/wiki/Archimedes%27_principle" title="Archimedes' principle">Archimedes' principle</a> <b>·</b> <a href="/wiki/Bernoulli%27s_principle" title="Bernoulli's principle">Bernoulli's principle</a></li> <li><a href="/wiki/Navier%E2%80%93Stokes_equations" title="Navier–Stokes equations">Navier–Stokes equations</a></li> <li><a href="/wiki/Hagen%E2%80%93Poiseuille_equation" title="Hagen–Poiseuille equation">Poiseuille equation</a> <b>·</b> <a href="/wiki/Pascal%27s_law" title="Pascal's law">Pascal's law</a></li> <li><a href="/wiki/Viscosity" title="Viscosity">Viscosity</a> <ul><li>(<a href="/wiki/Newtonian_fluid" title="Newtonian fluid">Newtonian</a> <b>·</b> <a href="/wiki/Non-Newtonian_fluid" title="Non-Newtonian fluid">non-Newtonian</a>)</li></ul></li> <li><a href="/wiki/Buoyancy" title="Buoyancy">Buoyancy</a> <b>·</b> <a href="/wiki/Mixing_(process_engineering)" title="Mixing (process engineering)">Mixing</a> <b>·</b> <a href="/wiki/Pressure" title="Pressure">Pressure</a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;"> <a class="mw-selflink selflink">Liquids</a></th></tr><tr><td class="sidebar-content"> <div class="hlist"> <ul><li><a href="/wiki/Adhesion" title="Adhesion">Adhesion</a></li> <li><a href="/wiki/Capillary_action" title="Capillary action">Capillary action</a></li> <li><a href="/wiki/Chromatography" title="Chromatography">Chromatography</a></li> <li><a href="/wiki/Cohesion_(chemistry)" title="Cohesion (chemistry)">Cohesion (chemistry)</a></li> <li><a href="/wiki/Surface_tension" title="Surface tension">Surface tension</a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;"> <a href="/wiki/Gas" title="Gas">Gases</a></th></tr><tr><td class="sidebar-content"> <div class="hlist"> <ul><li><a href="/wiki/Atmosphere" title="Atmosphere">Atmosphere</a></li> <li><a href="/wiki/Boyle%27s_law" title="Boyle's law">Boyle's law</a></li> <li><a href="/wiki/Charles%27s_law" title="Charles's law">Charles's law</a></li> <li><a href="/wiki/Combined_gas_law" class="mw-redirect" title="Combined gas law">Combined gas law</a></li> <li><a href="/wiki/Fick%27s_law" class="mw-redirect" title="Fick's law">Fick's law</a></li> <li><a href="/wiki/Gay-Lussac%27s_law" title="Gay-Lussac's law">Gay-Lussac's law</a></li> <li><a href="/wiki/Graham%27s_law" title="Graham's law">Graham's law</a></li></ul> </div></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;"> <a href="/wiki/Plasma_(physics)" title="Plasma (physics)">Plasma</a></th></tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content-with-subgroup"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Rheology" title="Rheology">Rheology</a></div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar-subgroup"><tbody><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Viscoelasticity" title="Viscoelasticity">Viscoelasticity</a></li> <li><a href="/wiki/Rheometry" title="Rheometry">Rheometry</a></li> <li><a href="/wiki/Rheometer" title="Rheometer">Rheometer</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="font-style:italic;"> <a href="/wiki/Smart_fluid" title="Smart fluid">Smart fluids</a></th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Electrorheological_fluid" title="Electrorheological fluid">Electrorheological</a></li> <li><a href="/wiki/Magnetorheological_fluid" title="Magnetorheological fluid">Magnetorheological</a></li> <li><a href="/wiki/Ferrofluid" title="Ferrofluid">Ferrofluids</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)">Scientists</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist"> <ul><li><a href="/wiki/Daniel_Bernoulli" title="Daniel Bernoulli">Bernoulli</a></li> <li><a href="/wiki/Robert_Boyle" title="Robert Boyle">Boyle</a></li> <li><a href="/wiki/Augustin-Louis_Cauchy" title="Augustin-Louis Cauchy">Cauchy</a></li> <li><a href="/wiki/Jacques_Charles" title="Jacques Charles">Charles</a></li> <li><a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Euler</a></li> <li><a href="/wiki/Adolf_Eugen_Fick" title="Adolf Eugen Fick">Fick</a></li> <li><a href="/wiki/Joseph_Louis_Gay-Lussac" title="Joseph Louis Gay-Lussac">Gay-Lussac</a></li> <li><a href="/wiki/Thomas_Graham_(chemist)" title="Thomas Graham (chemist)">Graham</a></li> <li><a href="/wiki/Robert_Hooke" title="Robert Hooke">Hooke</a></li> <li><a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton</a></li> <li><a href="/wiki/Claude-Louis_Navier" title="Claude-Louis Navier">Navier</a></li> <li><a href="/wiki/Walter_Noll" title="Walter Noll">Noll</a></li> <li><a href="/wiki/Blaise_Pascal" title="Blaise Pascal">Pascal</a></li> <li><a href="/wiki/Sir_George_Stokes,_1st_Baronet" title="Sir George Stokes, 1st Baronet">Stokes</a></li> <li><a href="/wiki/Clifford_Truesdell" title="Clifford Truesdell">Truesdell</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Continuum_mechanics" title="Template:Continuum mechanics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Continuum_mechanics" title="Template talk:Continuum mechanics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Continuum_mechanics" title="Special:EditPage/Template:Continuum mechanics"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>A <b>liquid</b> is a nearly <a href="/wiki/Compressibility" title="Compressibility">incompressible</a> <a href="/wiki/Fluid" title="Fluid">fluid</a> that conforms to the shape of its container but retains a nearly constant volume independent of pressure. It is one of <a href="/wiki/State_of_matter#Four_fundamental_states" title="State of matter">the four fundamental states of matter</a> (the others being <a href="/wiki/Solid" title="Solid">solid</a>, <a href="/wiki/Gas" title="Gas">gas</a>, and <a href="/wiki/Plasma_(physics)" title="Plasma (physics)">plasma</a>), and is the only state with a definite volume but no fixed shape. </p><p>The <a href="/wiki/Density" title="Density">density</a> of a liquid is usually close to that of a solid, and much higher than that of a gas. Therefore, liquid and solid are both termed <a href="/wiki/Condensed_matter_physics" title="Condensed matter physics">condensed matter</a>. On the other hand, as liquids and gases share the ability to flow, they are both called fluids. </p><p>A liquid is made up of tiny vibrating particles of matter, such as atoms, held together by <a href="/wiki/Intermolecular_bonds" class="mw-redirect" title="Intermolecular bonds">intermolecular bonds</a>. Like a gas, a liquid is able to flow and take the shape of a container. Unlike a gas, a liquid maintains a fairly constant density and does not disperse to fill every space of a container. </p><p>Although liquid water is abundant on Earth, this state of matter is actually the least common in the known universe, because liquids require a relatively narrow temperature/pressure range to exist. Most known matter in the universe is either gas (as <a href="/wiki/Interstellar_cloud" title="Interstellar cloud">interstellar clouds</a>) or plasma (as <a href="/wiki/Star" title="Star">stars</a>). </p> <style data-mw-deduplicate="TemplateStyles:r886046785">.mw-parser-output .toclimit-2 .toclevel-1 ul,.mw-parser-output .toclimit-3 .toclevel-2 ul,.mw-parser-output .toclimit-4 .toclevel-3 ul,.mw-parser-output .toclimit-5 .toclevel-4 ul,.mw-parser-output .toclimit-6 .toclevel-5 ul,.mw-parser-output .toclimit-7 .toclevel-6 ul{display:none}</style><div class="toclimit-3"><meta property="mw:PageProp/toc" /></div> <div class="mw-heading mw-heading2"><h2 id="Introduction">Introduction</h2></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Hot_and_cold_water_immiscibility_thermal_image.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Hot_and_cold_water_immiscibility_thermal_image.jpg/220px-Hot_and_cold_water_immiscibility_thermal_image.jpg" decoding="async" width="220" height="188" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/4/4b/Hot_and_cold_water_immiscibility_thermal_image.jpg 1.5x" data-file-width="240" data-file-height="205" /></a><figcaption>Thermal image of a sink full of hot water with cold water being added, showing how the hot and the cold water flow into each other</figcaption></figure> <p>Liquid is one of the <a href="/wiki/State_of_matter" title="State of matter">four primary states of matter</a>, with the others being solid, gas and <a href="/wiki/Plasma_(physics)" title="Plasma (physics)">plasma</a>. A liquid is a <a href="/wiki/Fluid" title="Fluid">fluid</a>. Unlike a solid, the <a href="/wiki/Molecule" title="Molecule">molecules</a> in a liquid have a much greater freedom to move. The forces that bind the molecules together in a solid are only temporary in a liquid, allowing a liquid to flow while a solid remains rigid. </p><p>A liquid, like a gas, displays the properties of a fluid. A liquid can flow, assume the shape of a container, and, if placed in a sealed container, will distribute applied pressure evenly to every surface in the container. If liquid is placed in a bag, it can be squeezed into any shape. Unlike a gas, a liquid is nearly incompressible, meaning that it occupies nearly a constant volume over a wide range of pressures; it does not generally expand to fill available space in a container but forms its own surface, and it may not always mix readily with another liquid. These properties make a liquid suitable for applications such as <a href="/wiki/Hydraulics" title="Hydraulics">hydraulics</a>. </p><p>Liquid particles are bound firmly but not rigidly. They are able to move around one another freely, resulting in a limited degree of particle mobility. As the temperature increases, the increased vibrations of the molecules causes distances between the molecules to increase. When a liquid reaches its <a href="/wiki/Boiling_point" title="Boiling point">boiling point</a>, the cohesive forces that bind the molecules closely together break, and the liquid changes to its gaseous state (unless <a href="/wiki/Superheating" title="Superheating">superheating</a> occurs). If the temperature is decreased, the distances between the molecules become smaller. When the liquid reaches its <a href="/wiki/Melting_point" title="Melting point">freezing point</a> the molecules will usually lock into a very specific order, called crystallizing, and the bonds between them become more rigid, changing the liquid into its solid state (unless <a href="/wiki/Supercooling" title="Supercooling">supercooling</a> occurs). </p> <div class="mw-heading mw-heading2"><h2 id="Examples">Examples</h2></div> <p>Only two <a href="/wiki/Chemical_element" title="Chemical element">elements</a> are liquid at <a href="/wiki/Standard_conditions_for_temperature_and_pressure" class="mw-redirect" title="Standard conditions for temperature and pressure">standard conditions for temperature and pressure</a>: <a href="/wiki/Mercury_(element)" title="Mercury (element)">mercury</a> and <a href="/wiki/Bromine" title="Bromine">bromine</a>. Four more elements have melting points slightly above <a href="/wiki/Room_temperature" title="Room temperature">room temperature</a>: <a href="/wiki/Francium" title="Francium">francium</a>, <a href="/wiki/Caesium" title="Caesium">caesium</a>, <a href="/wiki/Gallium" title="Gallium">gallium</a> and <a href="/wiki/Rubidium" title="Rubidium">rubidium</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> In addition, certain mixtures of elements are liquid at room temperature, even if the individual elements are solid under the same conditions (see <a href="/wiki/Eutectic_mixture" class="mw-redirect" title="Eutectic mixture">eutectic mixture</a>). An example is the sodium-potassium metal alloy <a href="/wiki/NaK" class="mw-redirect" title="NaK">NaK</a>.<sup id="cite_ref-Leonchuk2022_2-0" class="reference"><a href="#cite_note-Leonchuk2022-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Other metal alloys that are liquid at room temperature include <a href="/wiki/Galinstan" title="Galinstan">galinstan</a>, which is a gallium-indium-tin alloy that melts at −19 °C (−2 °F), as well as some <a href="/wiki/Amalgam_(chemistry)" title="Amalgam (chemistry)">amalgams</a> (alloys involving mercury).<sup id="cite_ref-Surmann2005_3-0" class="reference"><a href="#cite_note-Surmann2005-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>Pure substances that are liquid under normal conditions include water, <a href="/wiki/Ethanol" title="Ethanol">ethanol</a> and many other organic solvents. Liquid water is of vital importance in chemistry and biology, and it is necessary for all known forms of life.<sup id="cite_ref-MottlGlazerKaiser2007_4-0" class="reference"><a href="#cite_note-MottlGlazerKaiser2007-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-ChybaHand2005_5-0" class="reference"><a href="#cite_note-ChybaHand2005-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>Inorganic liquids include water, <a href="/wiki/Magma" title="Magma">magma</a>, <a href="/wiki/Inorganic_nonaqueous_solvent" title="Inorganic nonaqueous solvent">inorganic nonaqueous solvents</a> and many <a href="/wiki/Acid" title="Acid">acids</a>. </p><p>Important everyday liquids include <a href="/wiki/Aqueous_solution" title="Aqueous solution">aqueous solutions</a> like household <a href="/wiki/Bleach" title="Bleach">bleach</a>, other <a href="/wiki/Mixture" title="Mixture">mixtures</a> of different substances such as <a href="/wiki/Mineral_oil" title="Mineral oil">mineral oil</a> and gasoline, <a href="/wiki/Emulsion" title="Emulsion">emulsions</a> like <a href="/wiki/Vinaigrette" title="Vinaigrette">vinaigrette</a> or <a href="/wiki/Mayonnaise" title="Mayonnaise">mayonnaise</a>, <a href="/wiki/Suspension_(chemistry)" title="Suspension (chemistry)">suspensions</a> like blood, and <a href="/wiki/Colloid" title="Colloid">colloids</a> like <a href="/wiki/Paint" title="Paint">paint</a> and <a href="/wiki/Milk" title="Milk">milk</a>. </p><p>Many gases can be <a href="/wiki/Liquefaction_of_gases" title="Liquefaction of gases">liquefied</a> by cooling, producing liquids such as <a href="/wiki/Liquid_oxygen" title="Liquid oxygen">liquid oxygen</a>, <a href="/wiki/Liquid_nitrogen" title="Liquid nitrogen">liquid nitrogen</a>, <a href="/wiki/Liquid_hydrogen" title="Liquid hydrogen">liquid hydrogen</a> and <a href="/wiki/Liquid_helium" title="Liquid helium">liquid helium</a>. Not all gases can be liquified at atmospheric pressure, however. <a href="/wiki/Carbon_dioxide" title="Carbon dioxide">Carbon dioxide</a>, for example, can only be liquified at pressures above 5.1 <a href="/wiki/Atmosphere_(unit)" class="mw-redirect" title="Atmosphere (unit)">atm</a>.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>Some materials cannot be classified within the classical three states of matter. For example, <a href="/wiki/Liquid_crystal" title="Liquid crystal">liquid crystals</a> (used in <a href="/wiki/Liquid-crystal_display" title="Liquid-crystal display">liquid-crystal displays</a>) possess both solid-like and liquid-like properties, and belong to their own state of matter distinct from either liquid or solid.<sup id="cite_ref-Andrienko2018_7-0" class="reference"><a href="#cite_note-Andrienko2018-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Blue_Lava_lamp.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Blue_Lava_lamp.JPG/220px-Blue_Lava_lamp.JPG" decoding="async" width="220" height="286" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Blue_Lava_lamp.JPG/330px-Blue_Lava_lamp.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Blue_Lava_lamp.JPG/440px-Blue_Lava_lamp.JPG 2x" data-file-width="2529" data-file-height="3293" /></a><figcaption>A <a href="/wiki/Lava_lamp" title="Lava lamp">lava lamp</a> contains two immiscible liquids (a molten wax and a watery solution) which add movement due to convection. In addition to the top surface, surfaces also form between the liquids, requiring a tension breaker to recombine the wax droplets at the bottom.</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Lubrication">Lubrication</h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Tribology" title="Tribology">Tribology</a></div> <p>Liquids are useful as <a href="/wiki/Lubricant" title="Lubricant">lubricants</a> due to their ability to form a thin, freely flowing layer between solid materials. Lubricants such as oil are chosen for <a href="/wiki/Viscosity" title="Viscosity">viscosity</a> and flow characteristics that are suitable throughout the <a href="/wiki/Operating_temperature" title="Operating temperature">operating temperature</a> range of the component. Oils are often used in engines, <a href="/wiki/Gear_box" class="mw-redirect" title="Gear box">gear boxes</a>, <a href="/wiki/Metalworking" title="Metalworking">metalworking</a>, and hydraulic systems for their good lubrication properties.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Solvation">Solvation</h3></div> <p>Many liquids are used as <a href="/wiki/Solvent" title="Solvent">solvents</a>, to dissolve other liquids or solids. <a href="/wiki/Solution_(chemistry)" title="Solution (chemistry)">Solutions</a> are found in a wide variety of applications, including <a href="/wiki/Paint" title="Paint">paints</a>, <a href="/wiki/Sealant" title="Sealant">sealants</a>, and <a href="/wiki/Adhesive" title="Adhesive">adhesives</a>. <a href="/wiki/Naphtha" title="Naphtha">Naphtha</a> and <a href="/wiki/Acetone" title="Acetone">acetone</a> are used frequently in industry to clean oil, grease, and tar from parts and machinery. <a href="/wiki/Body_fluid" title="Body fluid">Body fluids</a> are water-based solutions. </p><p><a href="/wiki/Surfactant" title="Surfactant">Surfactants</a> are commonly found in soaps and <a href="/wiki/Detergent" title="Detergent">detergents</a>. Solvents like alcohol are often used as <a href="/wiki/Antimicrobial" title="Antimicrobial">antimicrobials</a>. They are found in cosmetics, <a href="/wiki/Ink" title="Ink">inks</a>, and liquid <a href="/wiki/Dye_laser" title="Dye laser">dye lasers</a>. They are used in the food industry, in processes such as the extraction of <a href="/wiki/Vegetable_oil" title="Vegetable oil">vegetable oil</a>.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Cooling">Cooling</h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Water_cooling" title="Water cooling">Water cooling</a> and <a href="/wiki/Immersion_cooling" title="Immersion cooling">Immersion cooling</a></div> <p>Liquids tend to have better <a href="/wiki/Thermal_conductivity" class="mw-redirect" title="Thermal conductivity">thermal conductivity</a> than gases, and the ability to flow makes a liquid suitable for removing excess heat from mechanical components. The heat can be removed by channeling the liquid through a <a href="/wiki/Heat_exchanger" title="Heat exchanger">heat exchanger</a>, such as a <a href="/wiki/Radiator" title="Radiator">radiator</a>, or the heat can be removed with the liquid during <a href="/wiki/Evaporation" title="Evaporation">evaporation</a>.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> Water or <a href="/wiki/Glycol" class="mw-redirect" title="Glycol">glycol</a> coolants are used to keep engines from overheating.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> The coolants used in <a href="/wiki/Nuclear_reactor" title="Nuclear reactor">nuclear reactors</a> include water or liquid metals, such as <a href="/wiki/Sodium" title="Sodium">sodium</a> or <a href="/wiki/Bismuth" title="Bismuth">bismuth</a>.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Liquid_propellant" class="mw-redirect" title="Liquid propellant">Liquid propellant</a> films are used to cool the thrust chambers of <a href="/wiki/Rocket" title="Rocket">rockets</a>.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> In <a href="/wiki/Machining" title="Machining">machining</a>, water and oils are used to remove the excess heat generated, which can quickly ruin both the work piece and the tooling. During <a href="/wiki/Perspiration" title="Perspiration">perspiration</a>, sweat removes heat from the human body by evaporating. In the <a href="/wiki/Heating,_ventilation,_and_air-conditioning" class="mw-redirect" title="Heating, ventilation, and air-conditioning">heating, ventilation, and air-conditioning</a> industry (HVAC), liquids such as water are used to transfer heat from one area to another.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Cooking">Cooking</h3></div> <p>Liquids are often used in <a href="/wiki/Cooking" title="Cooking">cooking</a> due to their excellent heat-transfer capabilities. In addition to thermal conduction, liquids transmit energy by convection. In particular, because warmer fluids expand and rise while cooler areas contract and sink, liquids with low <a href="/wiki/Kinematic_viscosity" class="mw-redirect" title="Kinematic viscosity">kinematic viscosity</a> tend to transfer heat through <a href="/wiki/Convection" title="Convection">convection</a> at a fairly constant temperature, making a liquid suitable for <a href="/wiki/Blanching_(cooking)" title="Blanching (cooking)">blanching</a>, <a href="/wiki/Boiling" title="Boiling">boiling</a>, or <a href="/wiki/Frying" title="Frying">frying</a>. Even higher rates of heat transfer can be achieved by condensing a gas into a liquid. At the liquid's boiling point, all of the heat energy is used to cause the phase change from a liquid to a gas, without an accompanying increase in temperature, and is stored as chemical <a href="/wiki/Potential_energy" title="Potential energy">potential energy</a>. When the gas condenses back into a liquid this excess heat-energy is released at a constant temperature. This phenomenon is used in processes such as <a href="/wiki/Steaming" title="Steaming">steaming</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Distillation">Distillation</h3></div> <p>Since liquids often have different boiling points, mixtures or solutions of liquids or gases can typically be separated by <a href="/wiki/Distillation" title="Distillation">distillation</a>, using heat, cold, <a href="/wiki/Vacuum" title="Vacuum">vacuum</a>, pressure, or other means. Distillation can be found in everything from the production of <a href="/wiki/Alcoholic_beverage" title="Alcoholic beverage">alcoholic beverages</a>, to <a href="/wiki/Oil_refinery" title="Oil refinery">oil refineries</a>, to the <a href="/wiki/Air_separation" title="Air separation">cryogenic distillation</a> of gases such as <a href="/wiki/Argon" title="Argon">argon</a>, <a href="/wiki/Oxygen" title="Oxygen">oxygen</a>, <a href="/wiki/Nitrogen" title="Nitrogen">nitrogen</a>, <a href="/wiki/Neon" title="Neon">neon</a>, or <a href="/wiki/Xenon" title="Xenon">xenon</a> by <a href="/wiki/Liquefaction" title="Liquefaction">liquefaction</a> (cooling them below their individual boiling points).<sup id="cite_ref-Earle1983_15-0" class="reference"><a href="#cite_note-Earle1983-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Hydraulics">Hydraulics</h3></div> <p>Liquid is the primary component of <a href="/wiki/Hydraulic" class="mw-redirect" title="Hydraulic">hydraulic</a> systems, which take advantage of <a href="/wiki/Pascal%27s_law" title="Pascal's law">Pascal's law</a> to provide <a href="/wiki/Fluid_power" title="Fluid power">fluid power</a>. Devices such as <a href="/wiki/Pump" title="Pump">pumps</a> and <a href="/wiki/Waterwheel" class="mw-redirect" title="Waterwheel">waterwheels</a> have been used to change liquid motion into <a href="/wiki/Mechanical_work" class="mw-redirect" title="Mechanical work">mechanical work</a> since ancient times. Oils are forced through <a href="/wiki/Hydraulic_pump" title="Hydraulic pump">hydraulic pumps</a>, which transmit this force to <a href="/wiki/Hydraulic_cylinder" title="Hydraulic cylinder">hydraulic cylinders</a>. Hydraulics can be found in many applications, such as <a href="/wiki/Automotive_brakes" class="mw-redirect" title="Automotive brakes">automotive brakes</a> and <a href="/wiki/Automotive_transmission" class="mw-redirect" title="Automotive transmission">transmissions</a>, <a href="/wiki/Heavy_equipment_(construction)" class="mw-redirect" title="Heavy equipment (construction)">heavy equipment</a>, and airplane control systems. Various <a href="/wiki/Hydraulic_press" title="Hydraulic press">hydraulic presses</a> are used extensively in repair and manufacturing, for lifting, pressing, clamping and forming.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Liquid_metals">Liquid metals</h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Liquid_metal#Applications" title="Liquid metal">Liquid metal § Applications</a></div> <p>Liquid metals have several properties that are useful in <a href="/wiki/Sensor" title="Sensor">sensing</a> and <a href="/wiki/Actuator" title="Actuator">actuation</a>, particularly their <a href="/wiki/Electrical_conductivity" class="mw-redirect" title="Electrical conductivity">electrical conductivity</a> and ability to transmit forces (incompressibility). As freely flowing substances, liquid metals retain these bulk properties even under extreme deformation. For this reason, they have been proposed for use in <a href="/wiki/Soft_robotics" title="Soft robotics">soft robots</a> and <a href="/wiki/Wearable_technology" title="Wearable technology">wearable healthcare devices</a>, which must be able to operate under repeated deformation.<sup id="cite_ref-Dickey2017_17-0" class="reference"><a href="#cite_note-Dickey2017-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-ColeKhoshmaneshTang2021_18-0" class="reference"><a href="#cite_note-ColeKhoshmaneshTang2021-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> The metal <a href="/wiki/Gallium" title="Gallium">gallium</a> is considered to be a promising candidate for these applications as it is a liquid near room temperature, has low toxicity, and evaporates slowly.<sup id="cite_ref-TangTaborKalantar-ZadehDickey2021_19-0" class="reference"><a href="#cite_note-TangTaborKalantar-ZadehDickey2021-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Miscellaneous">Miscellaneous</h3></div> <p>Liquids are sometimes used in measuring devices. A <a href="/wiki/Thermometer" title="Thermometer">thermometer</a> often uses the <a href="/wiki/Thermal_expansion" title="Thermal expansion">thermal expansion</a> of liquids, such as <a href="/wiki/Mercury_(element)" title="Mercury (element)">mercury</a>, combined with their ability to flow to indicate temperature. A <a href="/wiki/Manometer" class="mw-redirect" title="Manometer">manometer</a> uses the weight of the liquid to indicate <a href="/wiki/Air_pressure" class="mw-redirect" title="Air pressure">air pressure</a>.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p><p>The free surface of a rotating liquid forms a circular <a href="/wiki/Paraboloid" title="Paraboloid">paraboloid</a> and can therefore be used as a <a href="/wiki/Telescope" title="Telescope">telescope</a>. These are known as <a href="/wiki/Liquid-mirror_telescope" title="Liquid-mirror telescope">liquid-mirror telescopes</a>.<sup id="cite_ref-Hickson1994_21-0" class="reference"><a href="#cite_note-Hickson1994-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> They are significantly cheaper than conventional telescopes,<sup id="cite_ref-Hickson2007_22-0" class="reference"><a href="#cite_note-Hickson2007-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> but can only point straight upward (<a href="/wiki/Zenith_telescope" title="Zenith telescope">zenith telescope</a>). A common choice for the liquid is mercury. </p> <div class="mw-heading mw-heading2"><h2 id="Mechanical_properties">Mechanical properties</h2></div> <div class="mw-heading mw-heading3"><h3 id="Volume">Volume</h3></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Cavitating-prop.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/66/Cavitating-prop.jpg/220px-Cavitating-prop.jpg" decoding="async" width="220" height="175" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/66/Cavitating-prop.jpg/330px-Cavitating-prop.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/66/Cavitating-prop.jpg/440px-Cavitating-prop.jpg 2x" data-file-width="753" data-file-height="600" /></a><figcaption>Cavitation in water from a boat propeller</figcaption></figure> <p>Quantities of liquids are measured in units of <a href="/wiki/Volume" title="Volume">volume</a>. These include the <a href="/wiki/International_System_of_Units" title="International System of Units">SI</a> unit cubic metre (m<sup>3</sup>) and its divisions, in particular the cubic decimeter, more commonly called the litre (1 dm<sup>3</sup> = 1 L = 0.001 m<sup>3</sup>), and the cubic centimetre, also called millilitre (1 cm<sup>3</sup> = 1 mL = 0.001 L = 10<sup>−6</sup> m<sup>3</sup>).<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p><p>The volume of a quantity of liquid is fixed by its temperature and <a href="/wiki/Pressure" title="Pressure">pressure</a>. Liquids generally expand when heated, and contract when cooled. Water between 0 °C and 4 °C is a notable exception.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p><p>On the other hand, liquids have little <a href="/wiki/Compressibility" title="Compressibility">compressibility</a>. Water, for example, will compress by only 46.4 parts per million for every unit increase in <a href="/wiki/Standard_atmospheric_pressure" class="mw-redirect" title="Standard atmospheric pressure">atmospheric pressure</a> (bar).<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> At around 4000 bar (400 <a href="/wiki/Megapascal" class="mw-redirect" title="Megapascal">megapascals</a> or 58,000 <a href="/wiki/Pounds_per_square_inch" class="mw-redirect" title="Pounds per square inch">psi</a>) of pressure at room temperature water experiences only an 11% decrease in volume.<sup id="cite_ref-ReferenceA_26-0" class="reference"><a href="#cite_note-ReferenceA-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> Incompressibility makes liquids suitable for <a href="/wiki/Hydraulics" title="Hydraulics">transmitting hydraulic power</a>, because a change in pressure at one point in a liquid is transmitted undiminished to every other part of the liquid and very little energy is lost in the form of compression.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> </p><p>However, the negligible compressibility does lead to other phenomena. The banging of pipes, called <a href="/wiki/Water_hammer" title="Water hammer">water hammer</a>, occurs when a valve is suddenly closed, creating a huge pressure-spike at the valve that travels backward through the system at just under the speed of sound. Another phenomenon caused by liquid's incompressibility is <a href="/wiki/Cavitation" title="Cavitation">cavitation</a>. Because liquids have little <a href="/wiki/Elasticity_(physics)" title="Elasticity (physics)">elasticity</a> they can literally be pulled apart in areas of high turbulence or dramatic change in direction, such as the trailing edge of a boat propeller or a sharp corner in a pipe. A liquid in an area of low pressure (vacuum) vaporizes and forms bubbles, which then collapse as they enter high pressure areas. This causes liquid to fill the cavities left by the bubbles with tremendous localized force, eroding any adjacent solid surface.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Pressure_and_buoyancy">Pressure and buoyancy</h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Fluid_statics" class="mw-redirect" title="Fluid statics">Fluid statics</a></div> <p>In a <a href="/wiki/Gravitational_field" title="Gravitational field">gravitational field</a>, liquids exert <a href="/wiki/Pressure" title="Pressure">pressure</a> on the sides of a container as well as on anything within the liquid itself. This pressure is transmitted in all directions and increases with depth. If a liquid is at rest in a uniform gravitational field, the pressure <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span> at depth <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf368e72c009decd9b6686ee84a375632e11de98" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.088ex; height:1.676ex;" alt="{\displaystyle z}"></span> is given by<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p=p_{0}+\rho gz\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>=</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mi>ρ</mi> <mi>g</mi> <mi>z</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p=p_{0}+\rho gz\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/abbb21a29e7dc3d87462b66cade9dfd24784aef5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:13.215ex; height:2.509ex;" alt="{\displaystyle p=p_{0}+\rho gz\,}"></span></dd></dl> <p>where: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p_{0}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{0}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75ebf555915465a60ea93f4c93f75eaf962f3a31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:2.7ex; height:2.009ex;" alt="{\displaystyle p_{0}\,}"></span> is the pressure at the surface</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a1d651c28959a0f15127c097ff4488b123d9e708" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.589ex; height:2.176ex;" alt="{\displaystyle \rho \,}"></span> is the <a href="/wiki/Density" title="Density">density</a> of the liquid, assumed uniform with depth</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>g</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ecc456e58b207759836214cb501a1aa1af3be5bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.503ex; height:2.009ex;" alt="{\displaystyle g\,}"></span> is the <a href="/wiki/Gravity" title="Gravity">gravitational acceleration</a></dd></dl> <p>For a body of water open to the air, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b969ada68a88e2aeba9a2d2096abaf1fd53c21d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:2.313ex; height:2.009ex;" alt="{\displaystyle p_{0}}"></span> would be the <a href="/wiki/Atmospheric_pressure" title="Atmospheric pressure">atmospheric pressure</a>. </p><p>Static liquids in uniform gravitational fields also exhibit the phenomenon of <a href="/wiki/Buoyancy" title="Buoyancy">buoyancy</a>, where objects immersed in the liquid experience a net force due to the pressure variation with depth. The magnitude of the force is equal to the weight of the liquid displaced by the object, and the direction of the force depends on the average density of the immersed object. If the density is <i>smaller</i> than that of the liquid, the buoyant force points <i>upward</i> and the object floats, whereas if the density is <i>larger</i>, the buoyant force points <i>downward</i> and the object sinks. This is known as <a href="/wiki/Archimedes%27_principle" title="Archimedes' principle">Archimedes' principle</a>.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Surfaces">Surfaces</h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Surface_tension" title="Surface tension">Surface tension</a> and <a href="/wiki/Surface_science" title="Surface science">Surface science</a></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:2006-01-14_Surface_waves.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/43/2006-01-14_Surface_waves.jpg/250px-2006-01-14_Surface_waves.jpg" decoding="async" width="250" height="172" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/43/2006-01-14_Surface_waves.jpg/375px-2006-01-14_Surface_waves.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/43/2006-01-14_Surface_waves.jpg/500px-2006-01-14_Surface_waves.jpg 2x" data-file-width="1920" data-file-height="1320" /></a><figcaption><a href="/wiki/Surface_wave" title="Surface wave">Surface waves</a> in water</figcaption></figure> <p>Unless the volume of a liquid exactly matches the volume of its container, one or more surfaces are observed. The presence of a surface introduces new phenomena which are not present in a bulk liquid. This is because a molecule at a surface possesses bonds with other liquid molecules only on the inner side of the surface, which implies a net force pulling surface molecules inward. Equivalently, this force can be described in terms of energy: there is a fixed amount of energy associated with forming a surface of a given area. This quantity is a material property called the <a href="/wiki/Surface_tension" title="Surface tension">surface tension</a>, in units of energy per unit area (SI units: <a href="/wiki/Joule" title="Joule">J</a>/<a href="/wiki/Meter" class="mw-redirect" title="Meter">m</a><sup>2</sup>). Liquids with strong intermolecular forces tend to have large surface tensions.<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> </p><p>A practical implication of surface tension is that liquids tend to minimize their surface area, forming spherical <a href="/wiki/Drop_(liquid)" title="Drop (liquid)">drops</a> and <a href="/wiki/Bubble_(physics)" title="Bubble (physics)">bubbles</a> unless other constraints are present. Surface tension is responsible for a range of other phenomena as well, including <a href="/wiki/Surface_wave" title="Surface wave">surface waves</a>, <a href="/wiki/Capillary_action" title="Capillary action">capillary action</a>, <a href="/wiki/Wetting" title="Wetting">wetting</a>, and <a href="/wiki/Capillary_wave" title="Capillary wave">ripples</a>. In liquids under <a href="/wiki/Confined_liquid" title="Confined liquid">nanoscale confinement</a>, surface effects can play a dominating role since – compared with a macroscopic sample of liquid – a much greater fraction of molecules are located near a surface. </p><p>The surface tension of a liquid directly affects its <a href="/wiki/Wettability" class="mw-redirect" title="Wettability">wettability</a>. Most common liquids have tensions ranging in the tens of mJ/m<sup>2</sup>, so droplets of oil, water, or glue can easily merge and adhere to other surfaces, whereas liquid metals such as mercury may have tensions ranging in the hundreds of mJ/m<sup>2</sup>, thus droplets do not combine easily and surfaces may only wet under specific conditions. </p><p>The surface tensions of common liquids occupy a relatively narrow range of values when exposed to changing conditions such as temperature, which contrasts strongly with the enormous variation seen in other mechanical properties, such as viscosity.<sup id="cite_ref-Bormashenko2018_32-0" class="reference"><a href="#cite_note-Bormashenko2018-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> </p><p>The <a href="/wiki/Free_surface" title="Free surface">free surface</a> of a liquid is disturbed by <a href="/wiki/Gravity" title="Gravity">gravity</a> (<a href="/wiki/Flatness_(liquids)" class="mw-redirect" title="Flatness (liquids)">flatness</a>) and <a href="/wiki/Water_waves" class="mw-redirect" title="Water waves">waves</a> (<a href="/wiki/Surface_roughness" title="Surface roughness">surface roughness</a>). </p> <div class="mw-heading mw-heading3"><h3 id="Flow">Flow</h3></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Viscosities.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Viscosities.gif/220px-Viscosities.gif" decoding="async" width="220" height="170" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Viscosities.gif/330px-Viscosities.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/44/Viscosities.gif/440px-Viscosities.gif 2x" data-file-width="600" data-file-height="463" /></a><figcaption>A simulation of <a href="/wiki/Viscosity" title="Viscosity">viscosity</a>. The fluid on the left has a lower viscosity and Newtonian behavior while the liquid on the right has higher viscosity and non-Newtonian behavior.</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Fluid_mechanics" title="Fluid mechanics">Fluid mechanics</a> and <a href="/wiki/Fluid_dynamics" title="Fluid dynamics">Fluid dynamics</a></div> <p>An important physical property characterizing the flow of liquids is <a href="/wiki/Viscosity" title="Viscosity">viscosity</a>. Intuitively, viscosity describes the resistance of a liquid to flow. </p><p>More technically, viscosity measures the resistance of a liquid to deformation at a given rate, such as when it is being sheared at finite velocity.<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> A specific example is a liquid flowing through a pipe: in this case the liquid undergoes shear deformation since it flows more slowly near the walls of the pipe than near the center. As a result, it exhibits viscous resistance to flow. In order to maintain flow, an external force must be applied, such as a pressure difference between the ends of the pipe. </p><p>The viscosity of liquids decreases with increasing temperature.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> </p><p>Precise control of viscosity is important in many applications, particularly the lubrication industry. One way to achieve such control is by blending two or more liquids of differing viscosities in precise ratios.<sup id="cite_ref-Zhmud2014_35-0" class="reference"><a href="#cite_note-Zhmud2014-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> In addition, various additives exist which can modulate the temperature-dependence of the viscosity of lubricating oils. This capability is important since machinery often operate over a range of temperatures (see also <a href="/wiki/Viscosity_index" title="Viscosity index">viscosity index</a>).<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> </p><p>The viscous behavior of a liquid can be either <a href="/wiki/Newtonian_fluid" title="Newtonian fluid">Newtonian</a> or <a href="/wiki/Non-Newtonian_fluid" title="Non-Newtonian fluid">non-Newtonian</a>. A Newtonian liquid exhibits a linear strain/stress curve, meaning its viscosity is independent of time, shear rate, or shear-rate history. Examples of Newtonian liquids include water, <a href="/wiki/Glycerin" class="mw-redirect" title="Glycerin">glycerin</a>, <a href="/wiki/Motor_oil" title="Motor oil">motor oil</a>, <a href="/wiki/Honey" title="Honey">honey</a>, or mercury. A non-Newtonian liquid is one where the viscosity is not independent of these factors and either thickens (increases in viscosity) or thins (decreases in viscosity) under shear. Examples of non-Newtonian liquids include <a href="/wiki/Ketchup" title="Ketchup">ketchup</a>, <a href="/wiki/Custard" title="Custard">custard</a>, or <a href="/wiki/Starch" title="Starch">starch</a> solutions.<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Sound_propagation">Sound propagation</h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Speed_of_sound#Speed_of_sound_in_liquids" title="Speed of sound">Speed of sound § Speed of sound in liquids</a></div> <p>The speed of sound in a liquid is given by <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c={\sqrt {K/\rho }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>ρ</mi> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c={\sqrt {K/\rho }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e2d7ce02ca3ae69204b70c149beec25f5c8aee0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:10.859ex; height:4.843ex;" alt="{\displaystyle c={\sqrt {K/\rho }}}"></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>K</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b76fce82a62ed5461908f0dc8f037de4e3686b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.066ex; height:2.176ex;" alt="{\displaystyle K}"></span> is the <a href="/wiki/Bulk_modulus" title="Bulk modulus">bulk modulus</a> of the liquid and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }"></span> the density. As an example, water has a bulk modulus of about 2.2 <a href="/wiki/Pascal_(unit)" title="Pascal (unit)">GPa</a> and a density of 1000 kg/m<sup>3</sup>, which gives <i>c</i> = 1.5 km/s.<sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Thermodynamics">Thermodynamics</h2></div> <div class="mw-heading mw-heading3"><h3 id="Phase_transitions">Phase transitions</h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Boiling" title="Boiling">Boiling</a>, <a href="/wiki/Boiling_point" title="Boiling point">Boiling point</a>, <a href="/wiki/Melting" title="Melting">Melting</a>, and <a href="/wiki/Melting_point" title="Melting point">Melting point</a></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Phase-diag2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/34/Phase-diag2.svg/300px-Phase-diag2.svg.png" decoding="async" width="300" height="251" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/34/Phase-diag2.svg/450px-Phase-diag2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/34/Phase-diag2.svg/600px-Phase-diag2.svg.png 2x" data-file-width="530" data-file-height="443" /></a><figcaption>A typical <a href="/wiki/Phase_diagram" title="Phase diagram">phase diagram</a>. The dotted line gives the anomalous behaviour of water. The green lines show how the <a href="/wiki/Freezing_point" class="mw-redirect" title="Freezing point">freezing point</a> can vary with pressure, and the blue line shows how the <a href="/wiki/Boiling_point" title="Boiling point">boiling point</a> can vary with pressure. The red line shows the boundary where <a href="/wiki/Sublimation_(chemistry)" class="mw-redirect" title="Sublimation (chemistry)">sublimation</a> or <a href="/wiki/Deposition_(physics)" class="mw-redirect" title="Deposition (physics)">deposition</a> can occur.</figcaption></figure> <p>At a temperature below the <a href="/wiki/Boiling_point" title="Boiling point">boiling point</a>, any matter in liquid form will evaporate until reaching equilibrium with the reverse process of condensation of its vapor. At this point the vapor will condense at the same rate as the liquid evaporates. Thus, a liquid cannot exist permanently if the evaporated liquid is continually removed.<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> A liquid at or above its boiling point will normally boil, though <a href="/wiki/Superheating" title="Superheating">superheating</a> can prevent this in certain circumstances. </p><p>At a temperature below the freezing point, a liquid will tend to <a href="/wiki/Crystallization" title="Crystallization">crystallize</a>, changing to its solid form. Unlike the transition to gas, there is no equilibrium at this transition under constant pressure,<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (February 2021)">citation needed</span></a></i>]</sup> so unless <a href="/wiki/Supercooling" title="Supercooling">supercooling</a> occurs, the liquid will eventually completely crystallize. However, this is only true under constant pressure, so that (for example) water and ice in a closed, strong container might reach an equilibrium where both phases coexist. For the opposite transition from solid to liquid, see <a href="/wiki/Melting" title="Melting">melting</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Liquids_in_space">Liquids in space</h3></div> <p>The phase diagram explains why liquids do not exist in space or any other vacuum. Since the pressure is essentially zero (except on surfaces or interiors of planets and moons) water and other liquids exposed to space will either immediately boil or freeze depending on the temperature. In regions of space near the Earth, water will freeze if the sun is not shining directly on it and vaporize (sublime) as soon as it is in sunlight. If water exists as ice on the Moon, it can only exist in shadowed holes where the sun never shines and where the surrounding rock does not heat it up too much. At some point near the orbit of Saturn, the light from the Sun is too faint to sublime ice to water vapor. This is evident from the longevity of the ice that composes Saturn's rings.<sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Solutions">Solutions</h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Solution_(chemistry)" title="Solution (chemistry)">Solution (chemistry)</a></div> <p>Liquids can form <a href="/wiki/Solution_(chemistry)" title="Solution (chemistry)">solutions</a> with gases, solids, and other liquids. </p><p>Two liquids are said to be <a href="/wiki/Miscible" class="mw-redirect" title="Miscible">miscible</a> if they can form a solution in any proportion; otherwise they are immiscible. As an example, water and <a href="/wiki/Ethanol" title="Ethanol">ethanol</a> (drinking alcohol) are miscible whereas water and <a href="/wiki/Gasoline" title="Gasoline">gasoline</a> are immiscible.<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> In some cases a mixture of otherwise immiscible liquids can be stabilized to form an <a href="/wiki/Emulsion" title="Emulsion">emulsion</a>, where one liquid is dispersed throughout the other as microscopic droplets. Usually this requires the presence of a <a href="/wiki/Surfactant" title="Surfactant">surfactant</a> in order to stabilize the droplets. A familiar example of an emulsion is <a href="/wiki/Mayonnaise" title="Mayonnaise">mayonnaise</a>, which consists of a mixture of water and oil that is stabilized by <a href="/wiki/Lecithin" title="Lecithin">lecithin</a>, a substance found in <a href="/wiki/Yolk" title="Yolk">egg yolks</a>.<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Microscopic_description">Microscopic description</h2></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Structure_of_liquids_and_glasses" title="Structure of liquids and glasses">Structure of liquids and glasses</a></div> <p>The microscopic structure of liquids is complex and historically has been the subject of intense research and debate.<sup id="cite_ref-Chandler2017_43-0" class="reference"><a href="#cite_note-Chandler2017-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-TrachenkoBrazhkin2015_44-0" class="reference"><a href="#cite_note-TrachenkoBrazhkin2015-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Ben-Naim2009_45-0" class="reference"><a href="#cite_note-Ben-Naim2009-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Pothoczki2015_46-0" class="reference"><a href="#cite_note-Pothoczki2015-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> A few of the key ideas are explained below. </p> <div class="mw-heading mw-heading3"><h3 id="General_description">General description</h3></div> <p>Microscopically, liquids consist of a dense, disordered packing of molecules. This contrasts with the other two common phases of matter, gases and solids. Although gases are disordered, the molecules are well-separated in space and interact primarily through molecule-molecule collisions. Conversely, although the molecules in solids are densely packed, they usually fall into a regular structure, such as a <a href="/wiki/Crystalline_lattice" class="mw-redirect" title="Crystalline lattice">crystalline lattice</a> (<a href="/wiki/Glass" title="Glass">glasses</a> are a notable exception). </p> <div class="mw-heading mw-heading3"><h3 id="Short-range_ordering">Short-range ordering</h3></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Teilchenmodell_Fl%C3%BCssigkeit.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f1/Teilchenmodell_Fl%C3%BCssigkeit.svg/200px-Teilchenmodell_Fl%C3%BCssigkeit.svg.png" decoding="async" width="200" height="131" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f1/Teilchenmodell_Fl%C3%BCssigkeit.svg/300px-Teilchenmodell_Fl%C3%BCssigkeit.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f1/Teilchenmodell_Fl%C3%BCssigkeit.svg/400px-Teilchenmodell_Fl%C3%BCssigkeit.svg.png 2x" data-file-width="520" data-file-height="340" /></a><figcaption>Structure of a classical monatomic liquid. Atoms have many nearest neighbors in contact, yet no long-range order is present.</figcaption></figure> <p>While liquids do not exhibit <a href="/wiki/Order_and_disorder#Long-range_order" title="Order and disorder">long-range ordering</a> as in a crystalline lattice, they do possess <a href="/wiki/Short_range_order" title="Short range order">short-range order</a>, which persists over a few molecular diameters.<sup id="cite_ref-Maitland1981_47-0" class="reference"><a href="#cite_note-Maitland1981-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-GalloRovere2021_48-0" class="reference"><a href="#cite_note-GalloRovere2021-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> </p><p>In all liquids, excluded volume interactions induce short-range order in molecular positions (center-of-mass coordinates). Classical monatomic liquids like argon and krypton are the simplest examples. Such liquids can be modeled as disordered "heaps" of closely packed spheres, and the short-range order corresponds to the fact that nearest and next-nearest neighbors in a packing of spheres tend to be separated by integer multiples of the diameter.<sup id="cite_ref-Chandler1987_49-0" class="reference"><a href="#cite_note-Chandler1987-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Finney2013_50-0" class="reference"><a href="#cite_note-Finney2013-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> </p><p>In most liquids, molecules are not spheres, and intermolecular forces possess a directionality, i.e., they depend on the relative orientation of molecules. As a result, there is short-ranged orientational order in addition to the positional order mentioned above. Orientational order is especially important in <a href="/wiki/Hydrogen_bond" title="Hydrogen bond">hydrogen-bonded</a> liquids like water.<sup id="cite_ref-Finney2015_51-0" class="reference"><a href="#cite_note-Finney2015-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Ludwig2005_52-0" class="reference"><a href="#cite_note-Ludwig2005-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> The strength and directional nature of hydrogen bonds drives the formation of local "networks" or "clusters" of molecules. Due to the relative importance of thermal fluctuations in liquids (compared with solids), these structures are highly dynamic, continuously deforming, breaking, and reforming.<sup id="cite_ref-Chandler1987_49-1" class="reference"><a href="#cite_note-Chandler1987-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Finney2015_51-1" class="reference"><a href="#cite_note-Finney2015-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Energy_and_entropy">Energy and entropy</h3></div> <p>The microscopic features of liquids derive from an interplay between attractive intermolecular forces and <a href="/wiki/Entropic_force" title="Entropic force">entropic forces</a>.<sup id="cite_ref-Chandler2009_53-0" class="reference"><a href="#cite_note-Chandler2009-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup> </p><p>The attractive forces tend to pull molecules close together, and along with short-range repulsive interactions, they are the dominant forces behind the regular structure of solids. The entropic forces are not "forces" in the mechanical sense; rather, they describe the tendency of a system to maximize its <a href="/wiki/Entropy" title="Entropy">entropy</a> at fixed energy (see <a href="/wiki/Microcanonical_ensemble" title="Microcanonical ensemble">microcanonical ensemble</a>). Roughly speaking, entropic forces drive molecules apart from each other, maximizing the volume they occupy. Entropic forces dominant in gases and explain the tendency of gases to fill their containers. In liquids, by contrast, the intermolecular and entropic forces are comparable, so it is not possible to neglect one in favor of the other. Quantitatively, the binding energy between adjacent molecules is the same order of magnitude as the thermal energy <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k_{\text{B}}T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>B</mtext> </mrow> </msub> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{\text{B}}T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/852c8d0a63d15a2cbe2f2a57fdf32311130f6e45" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.243ex; height:2.509ex;" alt="{\displaystyle k_{\text{B}}T}"></span>.<sup id="cite_ref-HansenMcDonald2013_54-0" class="reference"><a href="#cite_note-HansenMcDonald2013-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="No_small_parameter">No small parameter</h4></div> <p>The competition between energy and entropy makes liquids difficult to model at the molecular level, as there is no idealized "reference state" that can serve as a starting point for tractable theoretical descriptions. Mathematically, there is no small parameter from which one can develop a systematic <a href="/wiki/Perturbation_theory" title="Perturbation theory">perturbation theory</a>.<sup id="cite_ref-TrachenkoBrazhkin2015_44-1" class="reference"><a href="#cite_note-TrachenkoBrazhkin2015-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> This situation contrasts with both gases and solids. For gases, the reference state is the <a href="/wiki/Ideal_gas" title="Ideal gas">ideal gas</a>, and the density can be used as a small parameter to construct a theory of real (nonideal) gases (see <a href="/wiki/Virial_expansion" title="Virial expansion">virial expansion</a>).<sup id="cite_ref-Kardar_2007_p._55-0" class="reference"><a href="#cite_note-Kardar_2007_p.-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup> For crystalline solids, the reference state is a perfect crystalline lattice, and possible small parameters are thermal motions and <a href="/wiki/Lattice_defect" class="mw-redirect" title="Lattice defect">lattice defects</a>.<sup id="cite_ref-Finney2015_51-2" class="reference"><a href="#cite_note-Finney2015-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Role_of_quantum_mechanics">Role of quantum mechanics</h3></div> <p>Like all known forms of matter, liquids are fundamentally <a href="/wiki/Quantum_mechanical" class="mw-redirect" title="Quantum mechanical">quantum mechanical</a>. However, under standard conditions (near room temperature and pressure), much of the macroscopic behavior of liquids can be understood in terms of <a href="/wiki/Classical_mechanics" title="Classical mechanics">classical mechanics</a>.<sup id="cite_ref-HansenMcDonald2013_54-1" class="reference"><a href="#cite_note-HansenMcDonald2013-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Gray1984_56-0" class="reference"><a href="#cite_note-Gray1984-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> The "classical picture" posits that the constituent molecules are discrete entities that interact through intermolecular forces according to <a href="/wiki/Newton%27s_laws_of_motion" title="Newton's laws of motion">Newton's laws of motion</a>. As a result, their macroscopic properties can be described using <a href="/wiki/Classical_statistical_mechanics" class="mw-redirect" title="Classical statistical mechanics">classical statistical mechanics</a>. While the intermolecular force law technically derives from quantum mechanics, it is usually understood as a model input to classical theory, obtained either from a fit to experimental data or from the <a href="/wiki/Classical_limit" title="Classical limit">classical limit</a> of a quantum mechanical description.<sup id="cite_ref-MarxHutter_2012_57-0" class="reference"><a href="#cite_note-MarxHutter_2012-57"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Maitland1981_47-1" class="reference"><a href="#cite_note-Maitland1981-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> An illustrative, though highly simplified example is a collection of spherical molecules interacting through a <a href="/wiki/Lennard-Jones_potential" title="Lennard-Jones potential">Lennard-Jones potential</a>.<sup id="cite_ref-HansenMcDonald2013_54-2" class="reference"><a href="#cite_note-HansenMcDonald2013-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> </p> <table class="wikitable floatright"> <caption>Table 1: Thermal de Broglie wavelengths <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Λ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ac0a4a98a414e3480335f9ba652d12571ec6733" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.613ex; height:2.176ex;" alt="{\displaystyle \Lambda }"></span> of selected liquids.<sup id="cite_ref-HansenMcDonald2013_54-3" class="reference"><a href="#cite_note-HansenMcDonald2013-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> Quantum effects are negligible when the ratio <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Lambda /a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Lambda /a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c36389055c72fab3f5976129f146fb7c5729e3cb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.005ex; height:2.843ex;" alt="{\displaystyle \Lambda /a}"></span> is small, where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> is the average distance between molecules. </caption> <tbody><tr> <th>Liquid </th> <th>Temperature (K) </th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Λ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ac0a4a98a414e3480335f9ba652d12571ec6733" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.613ex; height:2.176ex;" alt="{\displaystyle \Lambda }"></span> (nm) </th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Lambda /a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Lambda /a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c36389055c72fab3f5976129f146fb7c5729e3cb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.005ex; height:2.843ex;" alt="{\displaystyle \Lambda /a}"></span> </th></tr> <tr> <td>Hydrogen (H<sub>2</sub>) </td> <td>14.1 </td> <td>0.33 </td> <td>0.97 </td></tr> <tr> <td>Neon </td> <td>24.5 </td> <td>0.078 </td> <td>0.26 </td></tr> <tr> <td>Krypton </td> <td>116 </td> <td>0.018 </td> <td>0.046 </td></tr> <tr> <td><a href="/wiki/Carbon_tetrachloride" title="Carbon tetrachloride">Carbon tetrachloride</a> (CCl<sub>4</sub>) </td> <td>250 </td> <td>0.009 </td> <td>0.017 </td></tr> </tbody></table> <p>For the classical limit to apply, a necessary condition is that the thermal <a href="/wiki/De_Broglie_wavelength" class="mw-redirect" title="De Broglie wavelength">de Broglie wavelength</a>, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Lambda =\left({\frac {2\pi \hbar ^{2}}{mk_{\text{B}}T}}\right)^{1/2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Λ</mi> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> <msup> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mi>m</mi> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>B</mtext> </mrow> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Lambda =\left({\frac {2\pi \hbar ^{2}}{mk_{\text{B}}T}}\right)^{1/2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d257e090ad491f27912e7e1cef72f18c33e002e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:17.951ex; height:6.843ex;" alt="{\displaystyle \Lambda =\left({\frac {2\pi \hbar ^{2}}{mk_{\text{B}}T}}\right)^{1/2}}"></span></dd></dl> <p>is small compared with the length scale under consideration.<sup id="cite_ref-HansenMcDonald2013_54-4" class="reference"><a href="#cite_note-HansenMcDonald2013-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-58" class="reference"><a href="#cite_note-58"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup> Here, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \hbar }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi class="MJX-variant">ℏ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \hbar }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de68de3a92517953436c93b5a76461d49160cc41" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.306ex; height:2.176ex;" alt="{\displaystyle \hbar }"></span> is the <a href="/wiki/Planck_constant" title="Planck constant">Planck constant</a> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span> is the molecule's mass. Typical values of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Λ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ac0a4a98a414e3480335f9ba652d12571ec6733" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.613ex; height:2.176ex;" alt="{\displaystyle \Lambda }"></span> are about 0.01-0.1 nanometers (Table 1). Hence, a high-resolution model of liquid structure at the nanoscale may require quantum mechanical considerations. A notable example is hydrogen bonding in associated liquids like water,<sup id="cite_ref-Ceriotti2013_59-0" class="reference"><a href="#cite_note-Ceriotti2013-59"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Markland_Ceriotti2018_60-0" class="reference"><a href="#cite_note-Markland_Ceriotti2018-60"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup> where, due to the small mass of the proton, inherently quantum effects such as <a href="/wiki/Zero-point_motion" class="mw-redirect" title="Zero-point motion">zero-point motion</a> and <a href="/wiki/Quantum_tunneling" class="mw-redirect" title="Quantum tunneling">tunneling</a> are important.<sup id="cite_ref-Li2011_61-0" class="reference"><a href="#cite_note-Li2011-61"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup> </p><p>For a liquid to behave classically at the macroscopic level, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Λ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ac0a4a98a414e3480335f9ba652d12571ec6733" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.613ex; height:2.176ex;" alt="{\displaystyle \Lambda }"></span> must be small compared with the average distance <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a\approx \rho ^{-1/3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>≈</mo> <msup> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\approx \rho ^{-1/3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/13f4125e0fb7975cc2bb44b1ae06134b9c318900" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.507ex; height:3.343ex;" alt="{\displaystyle a\approx \rho ^{-1/3}}"></span> between molecules.<sup id="cite_ref-HansenMcDonald2013_54-5" class="reference"><a href="#cite_note-HansenMcDonald2013-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> That is, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\Lambda }{a}}\ll 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">Λ</mi> <mi>a</mi> </mfrac> </mrow> <mo>≪</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\Lambda }{a}}\ll 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/03a0d8d9efc43f2e65734e890b6388fae4e3f29f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.226ex; height:5.343ex;" alt="{\displaystyle {\frac {\Lambda }{a}}\ll 1}"></span></dd></dl> <p>Representative values of this ratio for a few liquids are given in Table 1. The conclusion is that quantum effects are important for liquids at low temperatures and with small <a href="/wiki/Molecular_mass" title="Molecular mass">molecular mass</a>.<sup id="cite_ref-HansenMcDonald2013_54-6" class="reference"><a href="#cite_note-HansenMcDonald2013-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Gray1984_56-1" class="reference"><a href="#cite_note-Gray1984-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> For dynamic processes, there is an additional timescale constraint: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau \gg {\frac {h}{k_{B}T}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ</mi> <mo>≫</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>h</mi> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau \gg {\frac {h}{k_{B}T}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d99d0b26ee7dda7d93d8aedf45619ebfe31c87d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:9.979ex; height:5.843ex;" alt="{\displaystyle \tau \gg {\frac {h}{k_{B}T}}}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38a7dcde9730ef0853809fefc18d88771f95206c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.202ex; height:1.676ex;" alt="{\displaystyle \tau }"></span> is the timescale of the process under consideration. For room-temperature liquids, the right-hand side is about 10<sup>−14</sup> seconds, which generally means that time-dependent processes involving translational motion can be described classically.<sup id="cite_ref-HansenMcDonald2013_54-7" class="reference"><a href="#cite_note-HansenMcDonald2013-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> </p><p>At extremely low temperatures, even the macroscopic behavior of certain liquids deviates from classical mechanics. Notable examples are hydrogen and helium. Due to their low temperature and mass, such liquids have a thermal de Broglie wavelength comparable to the average distance between molecules.<sup id="cite_ref-HansenMcDonald2013_54-8" class="reference"><a href="#cite_note-HansenMcDonald2013-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Dynamic_phenomena">Dynamic phenomena</h3></div> <p>The expression for the sound velocity of a liquid, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c={\sqrt {K/\rho }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>ρ</mi> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c={\sqrt {K/\rho }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e2d7ce02ca3ae69204b70c149beec25f5c8aee0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:10.859ex; height:4.843ex;" alt="{\displaystyle c={\sqrt {K/\rho }}}"></span>,</dd></dl> <p>contains the <a href="/wiki/Bulk_modulus" title="Bulk modulus">bulk modulus</a> <i>K</i>. If <i>K</i> is frequency-independent, then the liquid behaves as a linear medium, so that sound propagates without <a href="/wiki/Dissipation" title="Dissipation">dissipation</a> or <a href="/wiki/Mode_coupling" title="Mode coupling">mode coupling</a>. In reality, all liquids show some <a href="/wiki/Acoustic_dispersion" title="Acoustic dispersion">dispersion</a>: with increasing frequency, <i>K</i> crosses over from the low-frequency, liquid-like limit <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/44b0af6cafb690d3dbb0f3f30a032631338dc476" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.027ex; height:2.509ex;" alt="{\displaystyle K_{0}}"></span> to the high-frequency, solid-like limit <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{\infty }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K_{\infty }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab1648fcb43e75a0cfb456ba8f5f5ecf47df73cb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.848ex; height:2.509ex;" alt="{\displaystyle K_{\infty }}"></span>. In normal liquids, most of this crossover takes place at frequencies between GHz and THz, sometimes called <a href="/wiki/Hypersound" class="mw-redirect" title="Hypersound">hypersound</a>. </p><p>At sub-GHz frequencies, a normal liquid cannot sustain <a href="/wiki/Shear_wave" class="mw-redirect" title="Shear wave">shear waves</a>: the zero-frequency limit of the <a href="/wiki/Shear_modulus" title="Shear modulus">shear modulus</a> is 0. This is sometimes seen as the defining property of a liquid.<sup id="cite_ref-62" class="reference"><a href="#cite_note-62"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-63" class="reference"><a href="#cite_note-63"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup> However, like the bulk modulus <i>K</i>, the shear modulus <i>G</i> is also frequency-dependent and exhibits a similar crossover at hypersound frequencies. </p><p>According to <a href="/wiki/Linear_response_theory" class="mw-redirect" title="Linear response theory">linear response theory</a>, the Fourier transform of <i>K</i> or <i>G</i> describes how the system returns to equilibrium after an external perturbation; for this reason, the dispersion step in the GHz to THz region is also called <a href="/wiki/Relaxation_(physics)" title="Relaxation (physics)">relaxation</a>. As a liquid is supercooled toward the glass transition, the structural relaxation time exponentially increases, which explains the viscoelastic behavior of glass-forming liquids. </p> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Lennard-Jones_Radial_Distribution_Function.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/Lennard-Jones_Radial_Distribution_Function.svg/300px-Lennard-Jones_Radial_Distribution_Function.svg.png" decoding="async" width="300" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/Lennard-Jones_Radial_Distribution_Function.svg/450px-Lennard-Jones_Radial_Distribution_Function.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/31/Lennard-Jones_Radial_Distribution_Function.svg/600px-Lennard-Jones_Radial_Distribution_Function.svg.png 2x" data-file-width="679" data-file-height="452" /></a><figcaption>Radial distribution function of the <a href="/wiki/Lennard-Jones_potential" title="Lennard-Jones potential">Lennard-Jones model fluid</a> </figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Experimental_methods">Experimental methods</h3></div> <p>The absence of long-range order in liquids is mirrored by the absence of <a href="/wiki/Bragg_peak" title="Bragg peak">Bragg peaks</a> in <a href="/wiki/X-ray_diffraction" title="X-ray diffraction">X-ray</a> and <a href="/wiki/Neutron_diffraction" title="Neutron diffraction">neutron diffraction</a>. Under normal conditions, the diffraction pattern has circular symmetry, expressing the <a href="/wiki/Isotropy" title="Isotropy">isotropy</a> of the liquid. Radially, the diffraction intensity smoothly oscillates. This can be described by the <a href="/wiki/Static_structure_factor" class="mw-redirect" title="Static structure factor">static structure factor</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S(q)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo stretchy="false">(</mo> <mi>q</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S(q)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5afeeb5ad0b7d09d9c2aa1795e6bcfd7f15e6ba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.378ex; height:2.843ex;" alt="{\displaystyle S(q)}"></span>, with wavenumber <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q=(4\pi /\lambda )\sin \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>q</mi> <mo>=</mo> <mo stretchy="false">(</mo> <mn>4</mn> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>λ</mi> <mo stretchy="false">)</mo> <mi>sin</mi> <mo>⁡</mo> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q=(4\pi /\lambda )\sin \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0db74992f79a6330dd386964cad9949233f90e99" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.71ex; height:2.843ex;" alt="{\displaystyle q=(4\pi /\lambda )\sin \theta }"></span> given by the wavelength <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b43d0ea3c9c025af1be9128e62a18fa74bedda2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.355ex; height:2.176ex;" alt="{\displaystyle \lambda }"></span> of the probe (photon or neutron) and the <a href="/wiki/Bragg_angle" class="mw-redirect" title="Bragg angle">Bragg angle</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }"></span>. The oscillations of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S(q)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo stretchy="false">(</mo> <mi>q</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S(q)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5afeeb5ad0b7d09d9c2aa1795e6bcfd7f15e6ba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.378ex; height:2.843ex;" alt="{\displaystyle S(q)}"></span> express the short-range order of the liquid, i.e., the correlations between a molecule and "shells" of nearest neighbors, next-nearest neighbors, and so on. </p><p>An equivalent representation of these correlations is the <a href="/wiki/Radial_distribution_function" title="Radial distribution function">radial distribution function</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g(r)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>g</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g(r)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e09e9ec780782afb0b2ae8c172811dba1e4eb63c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.974ex; height:2.843ex;" alt="{\displaystyle g(r)}"></span>, which is related to the <a href="/wiki/Fourier_transform" title="Fourier transform">Fourier transform</a> of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S(q)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo stretchy="false">(</mo> <mi>q</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S(q)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5afeeb5ad0b7d09d9c2aa1795e6bcfd7f15e6ba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.378ex; height:2.843ex;" alt="{\displaystyle S(q)}"></span>.<sup id="cite_ref-Chandler1987_49-2" class="reference"><a href="#cite_note-Chandler1987-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> It represents a spatial average of a temporal snapshot of pair correlations in the liquid. </p> <div class="mw-heading mw-heading2"><h2 id="Prediction_of_liquid_properties">Prediction of liquid properties</h2></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Computational_materials_science" title="Computational materials science">Computational materials science</a></div> <p>Methods for predicting liquid properties can be organized by their "scale" of description, that is, the <a href="/wiki/Length_scale" title="Length scale">length scales</a> and time scales over which they apply.<sup id="cite_ref-Krüger2016_64-0" class="reference"><a href="#cite_note-Krüger2016-64"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Steinhauser2022_65-0" class="reference"><a href="#cite_note-Steinhauser2022-65"><span class="cite-bracket">[</span>65<span class="cite-bracket">]</span></a></sup> </p> <ul><li><b>Macroscopic methods</b> use equations that directly model the large-scale behavior of liquids, such as their thermodynamic properties and flow behavior.</li> <li><b>Microscopic methods</b> use equations that model the dynamics of individual molecules.</li> <li><b>Mesoscopic methods</b> fall in between, combining elements of both continuum and particle-based models.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Macroscopic">Macroscopic</h3></div> <div class="mw-heading mw-heading4"><h4 id="Empirical_correlations">Empirical correlations</h4></div> <p>Empirical correlations are simple mathematical expressions intended to approximate a liquid's properties over a range of experimental conditions, such as varying temperature and pressure.<sup id="cite_ref-Poling2001_66-0" class="reference"><a href="#cite_note-Poling2001-66"><span class="cite-bracket">[</span>66<span class="cite-bracket">]</span></a></sup> They are constructed by <a href="/wiki/Regression_analysis" title="Regression analysis">fitting</a> simple functional forms to experimental data. For example, the <a href="/wiki/Temperature_dependence_of_viscosity" title="Temperature dependence of viscosity">temperature-dependence of liquid viscosity</a> is sometimes approximated by the function <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \eta (T)=Ae^{B/T}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>η</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>A</mi> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>T</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \eta (T)=Ae^{B/T}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c9c3017e49a6ba6745762517070f7cf1e4500d22" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.999ex; height:3.343ex;" alt="{\displaystyle \eta (T)=Ae^{B/T}}"></span>, where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span> are fitting constants.<sup id="cite_ref-67" class="reference"><a href="#cite_note-67"><span class="cite-bracket">[</span>67<span class="cite-bracket">]</span></a></sup> Empirical correlations allow for extremely efficient estimates of physical properties, which can be useful in thermophysical simulations. However, they require high quality experimental data to obtain a good fit and cannot reliably extrapolate beyond the conditions covered by experiments. </p> <div class="mw-heading mw-heading4"><h4 id="Thermodynamic_potentials">Thermodynamic potentials</h4></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Equation_of_state" title="Equation of state">Equation of state</a></div> <p>Thermodynamic potentials are functions that characterize the <a href="/wiki/Equilibrium_state" class="mw-redirect" title="Equilibrium state">equilibrium state</a> of a substance. An example is the <a href="/wiki/Gibbs_free_energy" title="Gibbs free energy">Gibbs free energy</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G(p,T)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mo stretchy="false">(</mo> <mi>p</mi> <mo>,</mo> <mi>T</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G(p,T)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ce9b07a107592e60b4d181593bd0a20ef222a506" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.476ex; height:2.843ex;" alt="{\displaystyle G(p,T)}"></span>, which is a function of pressure and temperature. Knowing any one thermodynamic potential <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {F}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">F</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {F}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/205d4b91000d9dcf1a5bbabdfa6a8395fa60b676" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.927ex; height:2.176ex;" alt="{\displaystyle {\mathcal {F}}}"></span> is sufficient to compute all equilibrium properties of a substance, often simply by taking <a href="/wiki/Derivative" title="Derivative">derivatives</a> of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {F}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">F</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {F}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/205d4b91000d9dcf1a5bbabdfa6a8395fa60b676" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.927ex; height:2.176ex;" alt="{\displaystyle {\mathcal {F}}}"></span>.<sup id="cite_ref-Kardar_2007_p._55-1" class="reference"><a href="#cite_note-Kardar_2007_p.-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup> Thus, a single correlation for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {F}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">F</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {F}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/205d4b91000d9dcf1a5bbabdfa6a8395fa60b676" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.927ex; height:2.176ex;" alt="{\displaystyle {\mathcal {F}}}"></span> can replace separate correlations for individual properties.<sup id="cite_ref-Span2000_68-0" class="reference"><a href="#cite_note-Span2000-68"><span class="cite-bracket">[</span>68<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Huber2022_69-0" class="reference"><a href="#cite_note-Huber2022-69"><span class="cite-bracket">[</span>69<span class="cite-bracket">]</span></a></sup> Conversely, a variety of experimental measurements (e.g., density, heat capacity, vapor pressure) can be incorporated into the same fit; in principle, this would allow one to predict hard-to-measure properties like heat capacity in terms of other, more readily available measurements (e.g., vapor pressure).<sup id="cite_ref-Tillner-Roth1998_70-0" class="reference"><a href="#cite_note-Tillner-Roth1998-70"><span class="cite-bracket">[</span>70<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Hydrodynamics">Hydrodynamics</h4></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Fluid_dynamics" title="Fluid dynamics">Fluid dynamics</a> and <a href="/wiki/Computational_fluid_dynamics" title="Computational fluid dynamics">Computational fluid dynamics</a></div> <p>Hydrodynamic theories describe liquids in terms of space- and time-dependent macroscopic <a href="/wiki/Field_(physics)" title="Field (physics)">fields</a>, such as density, velocity, and temperature. These fields obey <a href="/wiki/Partial_differential_equation" title="Partial differential equation">partial differential equations</a>, which can be linear or <a href="/wiki/Nonlinear_partial_differential_equation" title="Nonlinear partial differential equation">nonlinear</a>.<sup id="cite_ref-PrincetonCompanion_71-0" class="reference"><a href="#cite_note-PrincetonCompanion-71"><span class="cite-bracket">[</span>71<span class="cite-bracket">]</span></a></sup> Hydrodynamic theories are more general than equilibrium thermodynamic descriptions, which assume that liquids are approximately <a href="/wiki/Homogeneous" class="mw-redirect" title="Homogeneous">homogeneous</a> and time-independent. The Navier-Stokes equations are a well-known example: they are partial differential equations giving the time evolution of density, velocity, and temperature of a viscous fluid. There are numerous methods for numerically solving the Navier-Stokes equations and its variants.<sup id="cite_ref-Wendt2008_72-0" class="reference"><a href="#cite_note-Wendt2008-72"><span class="cite-bracket">[</span>72<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Pozrikidis2011_73-0" class="reference"><a href="#cite_note-Pozrikidis2011-73"><span class="cite-bracket">[</span>73<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Mesoscopic">Mesoscopic</h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Mesoscopic_physics" title="Mesoscopic physics">Mesoscopic physics</a></div> <p>Mesoscopic methods operate on length and time scales between the particle and continuum levels. For this reason, they combine elements of particle-based dynamics and continuum hydrodynamics.<sup id="cite_ref-Krüger2016_64-1" class="reference"><a href="#cite_note-Krüger2016-64"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup> </p><p>An example is the <a href="/wiki/Lattice_Boltzmann_methods" title="Lattice Boltzmann methods">lattice Boltzmann method</a>, which models a fluid as a collection of fictitious particles that exist on a lattice.<sup id="cite_ref-Krüger2016_64-2" class="reference"><a href="#cite_note-Krüger2016-64"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup> The particles evolve in time through streaming (straight-line motion) and <a href="/wiki/Collision" title="Collision">collisions</a>. Conceptually, it is based on the <a href="/wiki/Boltzmann_equation" title="Boltzmann equation">Boltzmann equation</a> for dilute gases, where the dynamics of a molecule consists of free motion interrupted by discrete binary collisions, but it is also applied to liquids. Despite the analogy with individual molecular trajectories, it is a coarse-grained description that typically operates on length and time scales larger than those of true molecular dynamics (hence the notion of "fictitious" particles). </p><p>Other methods that combine elements of continuum and particle-level dynamics include <a href="/wiki/Smoothed-particle_hydrodynamics" title="Smoothed-particle hydrodynamics">smoothed-particle hydrodynamics</a>,<sup id="cite_ref-Monaghan2005_74-0" class="reference"><a href="#cite_note-Monaghan2005-74"><span class="cite-bracket">[</span>74<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Lind2020_75-0" class="reference"><a href="#cite_note-Lind2020-75"><span class="cite-bracket">[</span>75<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Dissipative_particle_dynamics" title="Dissipative particle dynamics">dissipative particle dynamics</a>,<sup id="cite_ref-Español2017_76-0" class="reference"><a href="#cite_note-Español2017-76"><span class="cite-bracket">[</span>76<span class="cite-bracket">]</span></a></sup> and <a href="/w/index.php?title=Multiparticle_collision_dynamics&action=edit&redlink=1" class="new" title="Multiparticle collision dynamics (page does not exist)">multiparticle collision dynamics</a>.<sup id="cite_ref-Gompper2008_77-0" class="reference"><a href="#cite_note-Gompper2008-77"><span class="cite-bracket">[</span>77<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Microscopic">Microscopic</h3></div> <p>Microscopic simulation methods work directly with the equations of motion (classical or quantum) of the constituent molecules. </p> <div class="mw-heading mw-heading4"><h4 id="Classical_molecular_dynamics">Classical molecular dynamics</h4></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Molecular_dynamics" title="Molecular dynamics">Molecular dynamics</a> and <a href="/wiki/Molecular_mechanics" title="Molecular mechanics">Molecular mechanics</a></div> <p>Classical molecular dynamics (MD) simulates liquids using Newton's law of motion; from <a href="/wiki/Newton%27s_second_law" class="mw-redirect" title="Newton's second law">Newton's second law</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F=m{\ddot {x}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo>¨</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F=m{\ddot {x}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c1b96d67eb79c82b662746df16c78f400fa87e01" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.209ex; height:2.176ex;" alt="{\displaystyle F=m{\ddot {x}}}"></span>), the trajectories of molecules can be traced out explicitly and used to compute macroscopic liquid properties like density or viscosity. However, classical MD requires expressions for the <a href="/wiki/Interatomic_potential" title="Interatomic potential">intermolecular forces</a> ("<i>F</i>" in Newton's second law). Usually, these must be approximated using experimental data or some other input.<sup id="cite_ref-Maitland1981_47-2" class="reference"><a href="#cite_note-Maitland1981-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Ab_initio_(quantum)_molecular_dynamics"><span id="Ab_initio_.28quantum.29_molecular_dynamics"></span>Ab initio (quantum) molecular dynamics</h4></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Car%E2%80%93Parrinello_molecular_dynamics" title="Car–Parrinello molecular dynamics">Car–Parrinello molecular dynamics</a></div> <p>Ab initio quantum mechanical methods simulate liquids using only the laws of quantum mechanics and fundamental atomic constants.<sup id="cite_ref-MarxHutter_2012_57-1" class="reference"><a href="#cite_note-MarxHutter_2012-57"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup> In contrast with classical molecular dynamics, the intermolecular force fields are an output of the calculation, rather than an input based on experimental measurements or other considerations. In principle, ab initio methods can simulate the properties of a given liquid without any prior experimental data. However, they are very expensive computationally, especially for large molecules with internal structure. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 20em;"> <ul><li><a href="/wiki/Ionic_liquid" title="Ionic liquid">Ionic liquid</a></li> <li><a href="/wiki/Heavy_liquid" title="Heavy liquid">Heavy liquid</a></li> <li><a href="/wiki/Liquid_dielectric" title="Liquid dielectric">Liquid dielectric</a></li> <li><a href="/wiki/Liquid_marbles" title="Liquid marbles">Liquid marbles</a></li> <li><a href="/wiki/Liquid_breathing" title="Liquid breathing">Liquid breathing</a></li> <li><a href="/wiki/Liquid_resistor" title="Liquid resistor">Liquid resistor</a></li> <li><a href="/wiki/Microfluidics" title="Microfluidics">Microfluidics</a></li> <li><a href="/wiki/Fluidized_bed" title="Fluidized bed">Fluidized bed</a></li> <li><a href="/wiki/Supercritical_fluid" title="Supercritical fluid">Supercritical fluid</a></li></ul></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">Theodore Gray, The Elements: A Visual Exploration of Every Known Atom in the Universe New York: Workman Publishing, 2009, p. 127 <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1-57912-814-9" title="Special:BookSources/1-57912-814-9">1-57912-814-9</a></span> </li> <li id="cite_note-Leonchuk2022-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-Leonchuk2022_2-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLeonchukFalchevskayaNikolaevVinogradov2022" class="citation journal cs1">Leonchuk, Sergei S.; Falchevskaya, Aleksandra S.; Nikolaev, Vitaly; Vinogradov, Vladimir V. (2022). "NaK alloy: underrated liquid metal". <i>Journal of Materials Chemistry A</i>. <b>10</b> (43). Royal Society of Chemistry (RSC): 22955–22976. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1039%2Fd2ta06882f">10.1039/d2ta06882f</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/2050-7488">2050-7488</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:252979251">252979251</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Materials+Chemistry+A&rft.atitle=NaK+alloy%3A+underrated+liquid+metal&rft.volume=10&rft.issue=43&rft.pages=22955-22976&rft.date=2022&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A252979251%23id-name%3DS2CID&rft.issn=2050-7488&rft_id=info%3Adoi%2F10.1039%2Fd2ta06882f&rft.aulast=Leonchuk&rft.aufirst=Sergei+S.&rft.au=Falchevskaya%2C+Aleksandra+S.&rft.au=Nikolaev%2C+Vitaly&rft.au=Vinogradov%2C+Vladimir+V.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-Surmann2005-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-Surmann2005_3-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSurmannZeyat2005" class="citation journal cs1">Surmann, Peter; Zeyat, Hanan (2005-10-15). "Voltammetric analysis using a self-renewable non-mercury electrode". <i>Analytical and Bioanalytical Chemistry</i>. <b>383</b> (6). Springer Science and Business Media LLC: 1009–1013. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs00216-005-0069-7">10.1007/s00216-005-0069-7</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1618-2642">1618-2642</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/16228199">16228199</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:22732411">22732411</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Analytical+and+Bioanalytical+Chemistry&rft.atitle=Voltammetric+analysis+using+a+self-renewable+non-mercury+electrode&rft.volume=383&rft.issue=6&rft.pages=1009-1013&rft.date=2005-10-15&rft.issn=1618-2642&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A22732411%23id-name%3DS2CID&rft_id=info%3Apmid%2F16228199&rft_id=info%3Adoi%2F10.1007%2Fs00216-005-0069-7&rft.aulast=Surmann&rft.aufirst=Peter&rft.au=Zeyat%2C+Hanan&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-MottlGlazerKaiser2007-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-MottlGlazerKaiser2007_4-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMottlGlazerKaiserMeech2007" class="citation journal cs1">Mottl, Michael J.; Glazer, Brian T.; Kaiser, Ralf I.; Meech, Karen J. (December 2007). <a rel="nofollow" class="external text" href="https://www.soest.hawaii.edu/oceanography/glazer/Brian_T._Glazer/downloads/Mottl07a.pdf">"Water and astrobiology"</a> <span class="cs1-format">(PDF)</span>. <i>Geochemistry</i>. <b>67</b> (4): 253–282. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2007ChEG...67..253M">2007ChEG...67..253M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.chemer.2007.09.002">10.1016/j.chemer.2007.09.002</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0009-2819">0009-2819</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Geochemistry&rft.atitle=Water+and+astrobiology&rft.volume=67&rft.issue=4&rft.pages=253-282&rft.date=2007-12&rft.issn=0009-2819&rft_id=info%3Adoi%2F10.1016%2Fj.chemer.2007.09.002&rft_id=info%3Abibcode%2F2007ChEG...67..253M&rft.aulast=Mottl&rft.aufirst=Michael+J.&rft.au=Glazer%2C+Brian+T.&rft.au=Kaiser%2C+Ralf+I.&rft.au=Meech%2C+Karen+J.&rft_id=https%3A%2F%2Fwww.soest.hawaii.edu%2Foceanography%2Fglazer%2FBrian_T._Glazer%2Fdownloads%2FMottl07a.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-ChybaHand2005-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-ChybaHand2005_5-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChybaHand2005" class="citation journal cs1">Chyba, Christopher F.; Hand, Kevin P. (1 September 2005). "Astrobiology: The Study of the Living Universe". <i>Annual Review of Astronomy and Astrophysics</i>. <b>43</b> (1): 31–74. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2005ARA&A..43...31C">2005ARA&A..43...31C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1146%2Fannurev.astro.43.051804.102202">10.1146/annurev.astro.43.051804.102202</a>. <a href="/wiki/EISSN_(identifier)" class="mw-redirect" title="EISSN (identifier)">eISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1545-4282">1545-4282</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0066-4146">0066-4146</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annual+Review+of+Astronomy+and+Astrophysics&rft.atitle=Astrobiology%3A+The+Study+of+the+Living+Universe&rft.volume=43&rft.issue=1&rft.pages=31-74&rft.date=2005-09-01&rft_id=info%3Adoi%2F10.1146%2Fannurev.astro.43.051804.102202&rft.issn=0066-4146&rft.eissn=1545-4282&rft_id=info%3Abibcode%2F2005ARA%26A..43...31C&rft.aulast=Chyba&rft.aufirst=Christopher+F.&rft.au=Hand%2C+Kevin+P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSilberberg2009" class="citation cs2">Silberberg, Martin S. (2009), <i>Chemistry: The Molecular Nature of Matter and Change</i>, McGraw-Hill Higher Education, pp. 448–449, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-304859-8" title="Special:BookSources/978-0-07-304859-8"><bdi>978-0-07-304859-8</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chemistry%3A+The+Molecular+Nature+of+Matter+and+Change&rft.pages=448-449&rft.pub=McGraw-Hill+Higher+Education&rft.date=2009&rft.isbn=978-0-07-304859-8&rft.aulast=Silberberg&rft.aufirst=Martin+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-Andrienko2018-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-Andrienko2018_7-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAndrienko2018" class="citation journal cs1">Andrienko, Denis (October 2018). <a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.molliq.2018.01.175">"Introduction to liquid crystals"</a>. <i>Journal of Molecular Liquids</i>. <b>267</b>: 520–541. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.molliq.2018.01.175">10.1016/j.molliq.2018.01.175</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0167-7322">0167-7322</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Molecular+Liquids&rft.atitle=Introduction+to+liquid+crystals&rft.volume=267&rft.pages=520-541&rft.date=2018-10&rft_id=info%3Adoi%2F10.1016%2Fj.molliq.2018.01.175&rft.issn=0167-7322&rft.aulast=Andrienko&rft.aufirst=Denis&rft_id=https%3A%2F%2Fdoi.org%2F10.1016%252Fj.molliq.2018.01.175&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text">Theo Mang, Wilfried Dressel <a rel="nofollow" class="external text" href="https://books.google.com/books?id=UTdfxf2rkNcC&"><i>Lubricants and lubrication</i></a>, Wiley-VCH 2007 <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/3-527-31497-0" title="Special:BookSources/3-527-31497-0">3-527-31497-0</a></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text">George Wypych <a rel="nofollow" class="external text" href="https://books.google.com/books?id=NzhUTvUkpDQC&pg=PA847"><i>Handbook of solvents</i></a> William Andrew Publishing 2001 pp. 847–881 <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1-895198-24-0" title="Special:BookSources/1-895198-24-0">1-895198-24-0</a></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text">N. B. Vargaftik <i>Handbook of thermal conductivity of liquids and gases</i> CRC Press 1994 <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8493-9345-0" title="Special:BookSources/0-8493-9345-0">0-8493-9345-0</a></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">Jack Erjavec <a rel="nofollow" class="external text" href="https://books.google.com/books?id=U4TBoJB2zgsC&pg=PA309"><i>Automotive technology: a systems approach</i></a> Delmar Learning 2000 p. 309 <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1-4018-4831-1" title="Special:BookSources/1-4018-4831-1">1-4018-4831-1</a></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text">Gerald Wendt <i>The prospects of nuclear power and technology</i> D. Van Nostrand Company 1957 p. 266</span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><i>Modern engineering for design of liquid-propellant rocket engines</i> by Dieter K. Huzel, David H. Huang – American Institute of Aeronautics and Astronautics 1992 p. 99 <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1-56347-013-6" title="Special:BookSources/1-56347-013-6">1-56347-013-6</a></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text">Thomas E Mull <i>HVAC principles and applications manual</i> McGraw-Hill 1997 <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-07-044451-X" title="Special:BookSources/0-07-044451-X">0-07-044451-X</a></span> </li> <li id="cite_note-Earle1983-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-Earle1983_15-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEarle1983" class="citation book cs1">Earle, R. L. (1983). <i>Unit operations in food processing</i>. Oxford: Pergamon Press. pp. 56–62, 138–141. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-08-025537-X" title="Special:BookSources/0-08-025537-X"><bdi>0-08-025537-X</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/8451210">8451210</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Unit+operations+in+food+processing&rft.place=Oxford&rft.pages=56-62%2C+138-141&rft.pub=Pergamon+Press&rft.date=1983&rft_id=info%3Aoclcnum%2F8451210&rft.isbn=0-08-025537-X&rft.aulast=Earle&rft.aufirst=R.+L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text">R. Keith Mobley <a rel="nofollow" class="external text" href="https://books.google.com/books?id=8DyLdlfJzoMC&pg=PA1"><i>Fluid power dynamics</i></a> Butterworth-Heinemann 2000 p. vii <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-7506-7174-2" title="Special:BookSources/0-7506-7174-2">0-7506-7174-2</a></span> </li> <li id="cite_note-Dickey2017-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-Dickey2017_17-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDickey2017" class="citation journal cs1">Dickey, Michael D. (2017-04-18). <a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fadma.201606425">"Stretchable and Soft Electronics using Liquid Metals"</a>. <i>Advanced Materials</i>. <b>29</b> (27). Wiley: 1606425. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2017AdM....2906425D">2017AdM....2906425D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fadma.201606425">10.1002/adma.201606425</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0935-9648">0935-9648</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/28417536">28417536</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:205276487">205276487</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Advanced+Materials&rft.atitle=Stretchable+and+Soft+Electronics+using+Liquid+Metals&rft.volume=29&rft.issue=27&rft.pages=1606425&rft.date=2017-04-18&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A205276487%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2017AdM....2906425D&rft.issn=0935-9648&rft_id=info%3Adoi%2F10.1002%2Fadma.201606425&rft_id=info%3Apmid%2F28417536&rft.aulast=Dickey&rft.aufirst=Michael+D.&rft_id=https%3A%2F%2Fdoi.org%2F10.1002%252Fadma.201606425&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-ColeKhoshmaneshTang2021-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-ColeKhoshmaneshTang2021_18-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFColeKhoshmaneshTang2021" class="citation journal cs1">Cole, Tim; Khoshmanesh, Khashayar; Tang, Shi-Yang (2021-05-04). "Liquid Metal Enabled Biodevices". <i>Advanced Intelligent Systems</i>. <b>3</b> (7). Wiley: 2000275. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Faisy.202000275">10.1002/aisy.202000275</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/2640-4567">2640-4567</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:235568215">235568215</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Advanced+Intelligent+Systems&rft.atitle=Liquid+Metal+Enabled+Biodevices&rft.volume=3&rft.issue=7&rft.pages=2000275&rft.date=2021-05-04&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A235568215%23id-name%3DS2CID&rft.issn=2640-4567&rft_id=info%3Adoi%2F10.1002%2Faisy.202000275&rft.aulast=Cole&rft.aufirst=Tim&rft.au=Khoshmanesh%2C+Khashayar&rft.au=Tang%2C+Shi-Yang&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-TangTaborKalantar-ZadehDickey2021-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-TangTaborKalantar-ZadehDickey2021_19-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTangTaborKalantar-ZadehDickey2021" class="citation journal cs1">Tang, Shi-Yang; Tabor, Christopher; Kalantar-Zadeh, Kourosh; Dickey, Michael D. (2021-07-26). <a rel="nofollow" class="external text" href="https://doi.org/10.1146%2Fannurev-matsci-080819-125403">"Gallium Liquid Metal: The Devil's Elixir"</a>. <i>Annual Review of Materials Research</i>. <b>51</b> (1). Annual Reviews: 381–408. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2021AnRMS..51..381T">2021AnRMS..51..381T</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1146%2Fannurev-matsci-080819-125403">10.1146/annurev-matsci-080819-125403</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1531-7331">1531-7331</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:236566966">236566966</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annual+Review+of+Materials+Research&rft.atitle=Gallium+Liquid+Metal%3A+The+Devil%27s+Elixir&rft.volume=51&rft.issue=1&rft.pages=381-408&rft.date=2021-07-26&rft_id=info%3Adoi%2F10.1146%2Fannurev-matsci-080819-125403&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A236566966%23id-name%3DS2CID&rft.issn=1531-7331&rft_id=info%3Abibcode%2F2021AnRMS..51..381T&rft.aulast=Tang&rft.aufirst=Shi-Yang&rft.au=Tabor%2C+Christopher&rft.au=Kalantar-Zadeh%2C+Kourosh&rft.au=Dickey%2C+Michael+D.&rft_id=https%3A%2F%2Fdoi.org%2F10.1146%252Fannurev-matsci-080819-125403&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text">Bela G. Liptak <a rel="nofollow" class="external text" href="https://books.google.com/books?id=pPMursVsxlMC&pg=PA807"><i>Instrument engineers' handbook: process control</i></a> CRC Press 1999 p. 807 <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8493-1081-4" title="Special:BookSources/0-8493-1081-4">0-8493-1081-4</a></span> </li> <li id="cite_note-Hickson1994-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-Hickson1994_21-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHicksonBorraCabanacContent1994" class="citation journal cs1">Hickson, Paul; Borra, Ermanno F.; Cabanac, Remi; Content, Robert; Gibson, Brad K.; Walker, Gordon A. H. (1994). "UBC/Laval 2.7 meter liquid mirror telescope". <i>The Astrophysical Journal</i>. <b>436</b>. American Astronomical Society: L201. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/9406057">astro-ph/9406057</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1994ApJ...436L.201H">1994ApJ...436L.201H</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F187667">10.1086/187667</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0004-637X">0004-637X</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Astrophysical+Journal&rft.atitle=UBC%2FLaval+2.7+meter+liquid+mirror+telescope&rft.volume=436&rft.pages=L201&rft.date=1994&rft_id=info%3Aarxiv%2Fastro-ph%2F9406057&rft.issn=0004-637X&rft_id=info%3Adoi%2F10.1086%2F187667&rft_id=info%3Abibcode%2F1994ApJ...436L.201H&rft.aulast=Hickson&rft.aufirst=Paul&rft.au=Borra%2C+Ermanno+F.&rft.au=Cabanac%2C+Remi&rft.au=Content%2C+Robert&rft.au=Gibson%2C+Brad+K.&rft.au=Walker%2C+Gordon+A.+H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-Hickson2007-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-Hickson2007_22-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHicksonRacine2007" class="citation journal cs1">Hickson, Paul; Racine, Réne (2007). <a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F517619">"Image Quality of Liquid‐Mirror Telescopes"</a>. <i>Publications of the Astronomical Society of the Pacific</i>. <b>119</b> (854). IOP Publishing: 456–465. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2007PASP..119..456H">2007PASP..119..456H</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F517619">10.1086/517619</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0004-6280">0004-6280</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:120735632">120735632</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Publications+of+the+Astronomical+Society+of+the+Pacific&rft.atitle=Image+Quality+of+Liquid%E2%80%90Mirror+Telescopes&rft.volume=119&rft.issue=854&rft.pages=456-465&rft.date=2007&rft_id=info%3Adoi%2F10.1086%2F517619&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A120735632%23id-name%3DS2CID&rft.issn=0004-6280&rft_id=info%3Abibcode%2F2007PASP..119..456H&rft.aulast=Hickson&rft.aufirst=Paul&rft.au=Racine%2C+R%C3%A9ne&rft_id=https%3A%2F%2Fdoi.org%2F10.1086%252F517619&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKnight2008" class="citation cs2">Knight, Randall D. (2008), <a rel="nofollow" class="external text" href="https://archive.org/details/physicsforscient0000knig/page/443"><i>Physics for Scientists and Engineers: A Strategic Approach (With Modern Physics)</i></a>, Addison-Wesley, p. <a rel="nofollow" class="external text" href="https://archive.org/details/physicsforscient0000knig/page/443">443</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8053-2736-6" title="Special:BookSources/978-0-8053-2736-6"><bdi>978-0-8053-2736-6</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physics+for+Scientists+and+Engineers%3A+A+Strategic+Approach+%28With+Modern+Physics%29&rft.pages=443&rft.pub=Addison-Wesley&rft.date=2008&rft.isbn=978-0-8053-2736-6&rft.aulast=Knight&rft.aufirst=Randall+D.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fphysicsforscient0000knig%2Fpage%2F443&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSilberberg2009" class="citation cs2">Silberberg, Martin S. (2009), <i>Chemistry: The Molecular Nature of Matter and Change</i>, McGraw-Hill Higher Education, p. 461, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-304859-8" title="Special:BookSources/978-0-07-304859-8"><bdi>978-0-07-304859-8</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chemistry%3A+The+Molecular+Nature+of+Matter+and+Change&rft.pages=461&rft.pub=McGraw-Hill+Higher+Education&rft.date=2009&rft.isbn=978-0-07-304859-8&rft.aulast=Silberberg&rft.aufirst=Martin+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://hyperphysics.phy-astr.gsu.edu/hbase/tables/compress.html">"Compressibility of Liquids"</a>. <i>hyperphysics.phy-astr.gsu.edu</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20171207161845/http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/compress.html">Archived</a> from the original on 7 December 2017<span class="reference-accessdate">. Retrieved <span class="nowrap">8 May</span> 2018</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=hyperphysics.phy-astr.gsu.edu&rft.atitle=Compressibility+of+Liquids&rft_id=http%3A%2F%2Fhyperphysics.phy-astr.gsu.edu%2Fhbase%2Ftables%2Fcompress.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-ReferenceA-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-ReferenceA_26-0">^</a></b></span> <span class="reference-text"><i>Intelligent Energy Field Manufacturing: Interdisciplinary Process Innovations</i> By Wenwu Zhang -- CRC Press 2011 Page 144</span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text">Knight (2008) p. 454</span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text"><i>Fluid Mechanics and Hydraulic Machines</i> by S. C. Gupta -- Dorling-Kindersley 2006 Page 85</span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text">Knight (2008) p. 448</span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text">Knight (2008) pp. 455-459</span> </li> <li id="cite_note-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-31">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSilberberg2009" class="citation cs2">Silberberg, Martin S. (2009), <i>Chemistry: The Molecular Nature of Matter and Change</i>, McGraw-Hill Higher Education, p. 457, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-304859-8" title="Special:BookSources/978-0-07-304859-8"><bdi>978-0-07-304859-8</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chemistry%3A+The+Molecular+Nature+of+Matter+and+Change&rft.pages=457&rft.pub=McGraw-Hill+Higher+Education&rft.date=2009&rft.isbn=978-0-07-304859-8&rft.aulast=Silberberg&rft.aufirst=Martin+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-Bormashenko2018-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-Bormashenko2018_32-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEdward_Yu._Bormashenko2018" class="citation book cs1"><a href="/wiki/Edward_Bormashenko" title="Edward Bormashenko">Edward Yu. Bormashenko</a> (5 November 2018). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=fwh2DwAAQBAJ&pg=PA3"><i>Wetting of Real Surfaces</i></a>. De Gruyter. pp. 3–5. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-11-058314-4" title="Special:BookSources/978-3-11-058314-4"><bdi>978-3-11-058314-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Wetting+of+Real+Surfaces&rft.pages=3-5&rft.pub=De+Gruyter&rft.date=2018-11-05&rft.isbn=978-3-11-058314-4&rft.au=Edward+Yu.+Bormashenko&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dfwh2DwAAQBAJ%26pg%3DPA3&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-33">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLandauLifshitz1987" class="citation cs2">Landau, L.D.; Lifshitz, E.M. (1987), <i>Fluid Mechanics</i> (2nd ed.), Pergamon Press, pp. 44–45, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-08-033933-7" title="Special:BookSources/978-0-08-033933-7"><bdi>978-0-08-033933-7</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fluid+Mechanics&rft.pages=44-45&rft.edition=2nd&rft.pub=Pergamon+Press&rft.date=1987&rft.isbn=978-0-08-033933-7&rft.aulast=Landau&rft.aufirst=L.D.&rft.au=Lifshitz%2C+E.M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-34">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBirdStewartLightfoot2007" class="citation cs2">Bird, R. Byron; Stewart, Warren E.; Lightfoot, Edwin N. (2007), <i>Transport Phenomena</i> (2nd ed.), John Wiley & Sons, Inc., p. 21, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-470-11539-8" title="Special:BookSources/978-0-470-11539-8"><bdi>978-0-470-11539-8</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Transport+Phenomena&rft.pages=21&rft.edition=2nd&rft.pub=John+Wiley+%26+Sons%2C+Inc.&rft.date=2007&rft.isbn=978-0-470-11539-8&rft.aulast=Bird&rft.aufirst=R.+Byron&rft.au=Stewart%2C+Warren+E.&rft.au=Lightfoot%2C+Edwin+N.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-Zhmud2014-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-Zhmud2014_35-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFZhmud2014" class="citation cs2">Zhmud, Boris (2014), <a rel="nofollow" class="external text" href="http://www.lube-media.com/wp-content/uploads/2017/11/Lube-Tech093-ViscosityBlendingEquations.pdf">"Viscosity Blending Equations"</a> <span class="cs1-format">(PDF)</span>, <i>Lube-Tech</i>, <b>93</b></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Lube-Tech&rft.atitle=Viscosity+Blending+Equations&rft.volume=93&rft.date=2014&rft.aulast=Zhmud&rft.aufirst=Boris&rft_id=http%3A%2F%2Fwww.lube-media.com%2Fwp-content%2Fuploads%2F2017%2F11%2FLube-Tech093-ViscosityBlendingEquations.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-36">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20200309134610/https://wiki.anton-paar.com/en/viscosity-index/">"Viscosity Index"</a>. UK: Anton Paar. Archived from <a rel="nofollow" class="external text" href="https://wiki.anton-paar.com/en/viscosity-index/">the original</a> on March 9, 2020<span class="reference-accessdate">. Retrieved <span class="nowrap">29 August</span> 2018</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Viscosity+Index&rft.place=UK&rft.pub=Anton+Paar&rft_id=https%3A%2F%2Fwiki.anton-paar.com%2Fen%2Fviscosity-index%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-37">^</a></b></span> <span class="reference-text"><i>Honey in Traditional and Modern Medicine</i> by Laid Boukraa -- CRC Press 2014 Page 22--24</span> </li> <li id="cite_note-38"><span class="mw-cite-backlink"><b><a href="#cite_ref-38">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTaylor2005" class="citation cs2">Taylor, John R. (2005), <i>Classical Mechanics</i>, University Science Books, pp. 727–729, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-891389-22-1" title="Special:BookSources/978-1-891389-22-1"><bdi>978-1-891389-22-1</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Classical+Mechanics&rft.pages=727-729&rft.pub=University+Science+Books&rft.date=2005&rft.isbn=978-1-891389-22-1&rft.aulast=Taylor&rft.aufirst=John+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-39"><span class="mw-cite-backlink"><b><a href="#cite_ref-39">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMarchTosi2002" class="citation cs2">March, N.H.; Tosi, M.P. (2002), <i>Introduction to Liquid State Physics</i>, World Scientific, p. 7, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2002ilsp.book.....M">2002ilsp.book.....M</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1142%2F4717">10.1142/4717</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-981-3102-53-8" title="Special:BookSources/978-981-3102-53-8"><bdi>978-981-3102-53-8</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Liquid+State+Physics&rft.pages=7&rft.pub=World+Scientific&rft.date=2002&rft_id=info%3Adoi%2F10.1142%2F4717&rft_id=info%3Abibcode%2F2002ilsp.book.....M&rft.isbn=978-981-3102-53-8&rft.aulast=March&rft.aufirst=N.H.&rft.au=Tosi%2C+M.P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-40"><span class="mw-cite-backlink"><b><a href="#cite_ref-40">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSiegel2014" class="citation web cs1">Siegel, Ethan (2014-12-11). <a rel="nofollow" class="external text" href="https://medium.com/starts-with-a-bang/does-water-freeze-or-boil-in-space-7889856d7f36">"Does water freeze or boil in space?"</a>. <i>Starts With A Bang!</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2022-02-10</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Starts+With+A+Bang%21&rft.atitle=Does+water+freeze+or+boil+in+space%3F&rft.date=2014-12-11&rft.aulast=Siegel&rft.aufirst=Ethan&rft_id=https%3A%2F%2Fmedium.com%2Fstarts-with-a-bang%2Fdoes-water-freeze-or-boil-in-space-7889856d7f36&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-41"><span class="mw-cite-backlink"><b><a href="#cite_ref-41">^</a></b></span> <span class="reference-text">Silberberg, pp. 188 and 502</span> </li> <li id="cite_note-42"><span class="mw-cite-backlink"><b><a href="#cite_ref-42">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMiodownik2019" class="citation cs2"><a href="/wiki/Mark_Miodownik" title="Mark Miodownik">Miodownik, Mark</a> (2019), <i>Liquid rules: The Delightful and Dangerous Substances that Flow Through Our Lives</i>, Houghton Mifflin Harcourt, p. 124, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-544-85019-4" title="Special:BookSources/978-0-544-85019-4"><bdi>978-0-544-85019-4</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Liquid+rules%3A+The+Delightful+and+Dangerous+Substances+that+Flow+Through+Our+Lives&rft.pages=124&rft.pub=Houghton+Mifflin+Harcourt&rft.date=2019&rft.isbn=978-0-544-85019-4&rft.aulast=Miodownik&rft.aufirst=Mark&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-Chandler2017-43"><span class="mw-cite-backlink"><b><a href="#cite_ref-Chandler2017_43-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChandler2017" class="citation journal cs1">Chandler, David (2017-05-05). "From 50 Years Ago, the Birth of Modern Liquid-State Science". <i>Annual Review of Physical Chemistry</i>. <b>68</b> (1). Annual Reviews: 19–38. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1609.04837">1609.04837</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2017ARPC...68...19C">2017ARPC...68...19C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1146%2Fannurev-physchem-052516-044941">10.1146/annurev-physchem-052516-044941</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0066-426X">0066-426X</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/28375691">28375691</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:37248336">37248336</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annual+Review+of+Physical+Chemistry&rft.atitle=From+50+Years+Ago%2C+the+Birth+of+Modern+Liquid-State+Science&rft.volume=68&rft.issue=1&rft.pages=19-38&rft.date=2017-05-05&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A37248336%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2017ARPC...68...19C&rft_id=info%3Aarxiv%2F1609.04837&rft.issn=0066-426X&rft_id=info%3Adoi%2F10.1146%2Fannurev-physchem-052516-044941&rft_id=info%3Apmid%2F28375691&rft.aulast=Chandler&rft.aufirst=David&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-TrachenkoBrazhkin2015-44"><span class="mw-cite-backlink">^ <a href="#cite_ref-TrachenkoBrazhkin2015_44-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-TrachenkoBrazhkin2015_44-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTrachenkoBrazhkin2015" class="citation journal cs1">Trachenko, K; Brazhkin, V V (2015-12-22). "Collective modes and thermodynamics of the liquid state". <i>Reports on Progress in Physics</i>. <b>79</b> (1). IOP Publishing: 016502. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1512.06592">1512.06592</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F0034-4885%2F79%2F1%2F016502">10.1088/0034-4885/79/1/016502</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0034-4885">0034-4885</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/26696098">26696098</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:42203015">42203015</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Reports+on+Progress+in+Physics&rft.atitle=Collective+modes+and+thermodynamics+of+the+liquid+state&rft.volume=79&rft.issue=1&rft.pages=016502&rft.date=2015-12-22&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A42203015%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1088%2F0034-4885%2F79%2F1%2F016502&rft_id=info%3Aarxiv%2F1512.06592&rft.issn=0034-4885&rft_id=info%3Apmid%2F26696098&rft.aulast=Trachenko&rft.aufirst=K&rft.au=Brazhkin%2C+V+V&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-Ben-Naim2009-45"><span class="mw-cite-backlink"><b><a href="#cite_ref-Ben-Naim2009_45-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBen-Naim2009" class="citation book cs1">Ben-Naim, Arieh (2009). <i>Molecular theory of water and aqueous solutions. Part 1, Understanding water</i>. Singapore: World Scientific. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-981-283-761-5" title="Special:BookSources/978-981-283-761-5"><bdi>978-981-283-761-5</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/696342117">696342117</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Molecular+theory+of+water+and+aqueous+solutions.+Part+1%2C+Understanding+water&rft.place=Singapore&rft.pub=World+Scientific&rft.date=2009&rft_id=info%3Aoclcnum%2F696342117&rft.isbn=978-981-283-761-5&rft.aulast=Ben-Naim&rft.aufirst=Arieh&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-Pothoczki2015-46"><span class="mw-cite-backlink"><b><a href="#cite_ref-Pothoczki2015_46-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPothoczkiTemleitnerPusztai2015" class="citation journal cs1">Pothoczki, Szilvia; Temleitner, László; Pusztai, László (2015-12-01). "Structure of Neat Liquids Consisting of (Perfect and Nearly) Tetrahedral Molecules". <i>Chemical Reviews</i>. <b>115</b> (24). American Chemical Society (ACS): 13308–13361. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Facs.chemrev.5b00308">10.1021/acs.chemrev.5b00308</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0009-2665">0009-2665</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/26624528">26624528</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Chemical+Reviews&rft.atitle=Structure+of+Neat+Liquids+Consisting+of+%28Perfect+and+Nearly%29+Tetrahedral+Molecules&rft.volume=115&rft.issue=24&rft.pages=13308-13361&rft.date=2015-12-01&rft.issn=0009-2665&rft_id=info%3Apmid%2F26624528&rft_id=info%3Adoi%2F10.1021%2Facs.chemrev.5b00308&rft.aulast=Pothoczki&rft.aufirst=Szilvia&rft.au=Temleitner%2C+L%C3%A1szl%C3%B3&rft.au=Pusztai%2C+L%C3%A1szl%C3%B3&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-Maitland1981-47"><span class="mw-cite-backlink">^ <a href="#cite_ref-Maitland1981_47-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Maitland1981_47-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Maitland1981_47-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMaitlandRigbySmithWakeham1981" class="citation book cs1">Maitland, Geoffrey C.; Rigby, Maurice; Smith, E. Brian; Wakeham, W. A. (1981). <i>Intermolecular forces: their origin and determination</i>. Oxford. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-19-855611-X" title="Special:BookSources/0-19-855611-X"><bdi>0-19-855611-X</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/8139179">8139179</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Intermolecular+forces%3A+their+origin+and+determination&rft.place=Oxford&rft.date=1981&rft_id=info%3Aoclcnum%2F8139179&rft.isbn=0-19-855611-X&rft.aulast=Maitland&rft.aufirst=Geoffrey+C.&rft.au=Rigby%2C+Maurice&rft.au=Smith%2C+E.+Brian&rft.au=Wakeham%2C+W.+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: location missing publisher (<a href="/wiki/Category:CS1_maint:_location_missing_publisher" title="Category:CS1 maint: location missing publisher">link</a>)</span></span> </li> <li id="cite_note-GalloRovere2021-48"><span class="mw-cite-backlink"><b><a href="#cite_ref-GalloRovere2021_48-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGalloRovere2021" class="citation book cs1">Gallo, Paola; Rovere, Mauro (2021). <i>Physics of liquid matter</i>. Cham: Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-030-68349-8" title="Special:BookSources/978-3-030-68349-8"><bdi>978-3-030-68349-8</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/1259588062">1259588062</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physics+of+liquid+matter&rft.place=Cham&rft.pub=Springer&rft.date=2021&rft_id=info%3Aoclcnum%2F1259588062&rft.isbn=978-3-030-68349-8&rft.aulast=Gallo&rft.aufirst=Paola&rft.au=Rovere%2C+Mauro&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-Chandler1987-49"><span class="mw-cite-backlink">^ <a href="#cite_ref-Chandler1987_49-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Chandler1987_49-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Chandler1987_49-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChandler1987" class="citation book cs1">Chandler, David (1987). <i>Introduction to modern statistical mechanics</i>. New York: Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-19-504276-X" title="Special:BookSources/0-19-504276-X"><bdi>0-19-504276-X</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/13946448">13946448</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+modern+statistical+mechanics&rft.place=New+York&rft.pub=Oxford+University+Press&rft.date=1987&rft_id=info%3Aoclcnum%2F13946448&rft.isbn=0-19-504276-X&rft.aulast=Chandler&rft.aufirst=David&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-Finney2013-50"><span class="mw-cite-backlink"><b><a href="#cite_ref-Finney2013_50-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFinney2013" class="citation journal cs1">Finney, John L. (2013-02-22). <a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F14786435.2013.770179">"Bernal's road to random packing and the structure of liquids"</a>. <i>Philosophical Magazine</i>. <b>93</b> (31–33). Informa UK Limited: 3940–3969. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2013PMag...93.3940F">2013PMag...93.3940F</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F14786435.2013.770179">10.1080/14786435.2013.770179</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1478-6435">1478-6435</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:55689631">55689631</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophical+Magazine&rft.atitle=Bernal%27s+road+to+random+packing+and+the+structure+of+liquids&rft.volume=93&rft.issue=31%E2%80%9333&rft.pages=3940-3969&rft.date=2013-02-22&rft_id=info%3Adoi%2F10.1080%2F14786435.2013.770179&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A55689631%23id-name%3DS2CID&rft.issn=1478-6435&rft_id=info%3Abibcode%2F2013PMag...93.3940F&rft.aulast=Finney&rft.aufirst=John+L.&rft_id=https%3A%2F%2Fdoi.org%2F10.1080%252F14786435.2013.770179&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-Finney2015-51"><span class="mw-cite-backlink">^ <a href="#cite_ref-Finney2015_51-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Finney2015_51-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Finney2015_51-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFinney2015" class="citation book cs1">Finney, J. L. (2015). <i>Water: a very short introduction</i>. Oxford, United Kingdom. pp. 48–52. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-870872-8" title="Special:BookSources/978-0-19-870872-8"><bdi>978-0-19-870872-8</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/914537747">914537747</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Water%3A+a+very+short+introduction&rft.place=Oxford%2C+United+Kingdom&rft.pages=48-52&rft.date=2015&rft_id=info%3Aoclcnum%2F914537747&rft.isbn=978-0-19-870872-8&rft.aulast=Finney&rft.aufirst=J.+L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: location missing publisher (<a href="/wiki/Category:CS1_maint:_location_missing_publisher" title="Category:CS1 maint: location missing publisher">link</a>)</span></span> </li> <li id="cite_note-Ludwig2005-52"><span class="mw-cite-backlink"><b><a href="#cite_ref-Ludwig2005_52-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLudwig2005" class="citation journal cs1">Ludwig, Ralf (2005-07-11). "The Structure of Liquid Methanol". <i>ChemPhysChem</i>. <b>6</b> (7). Wiley: 1369–1375. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fcphc.200400663">10.1002/cphc.200400663</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1439-4235">1439-4235</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/15991270">15991270</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=ChemPhysChem&rft.atitle=The+Structure+of+Liquid+Methanol&rft.volume=6&rft.issue=7&rft.pages=1369-1375&rft.date=2005-07-11&rft.issn=1439-4235&rft_id=info%3Apmid%2F15991270&rft_id=info%3Adoi%2F10.1002%2Fcphc.200400663&rft.aulast=Ludwig&rft.aufirst=Ralf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-Chandler2009-53"><span class="mw-cite-backlink"><b><a href="#cite_ref-Chandler2009_53-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChandler2009" class="citation journal cs1">Chandler, David (2009-09-08). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2741213">"Liquids: Condensed, disordered, and sometimes complex"</a>. <i>Proceedings of the National Academy of Sciences</i>. <b>106</b> (36): 15111–15112. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1073%2Fpnas.0908029106">10.1073/pnas.0908029106</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0027-8424">0027-8424</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2741213">2741213</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/19805248">19805248</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+National+Academy+of+Sciences&rft.atitle=Liquids%3A+Condensed%2C+disordered%2C+and+sometimes+complex&rft.volume=106&rft.issue=36&rft.pages=15111-15112&rft.date=2009-09-08&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC2741213%23id-name%3DPMC&rft.issn=0027-8424&rft_id=info%3Apmid%2F19805248&rft_id=info%3Adoi%2F10.1073%2Fpnas.0908029106&rft.aulast=Chandler&rft.aufirst=David&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC2741213&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-HansenMcDonald2013-54"><span class="mw-cite-backlink">^ <a href="#cite_ref-HansenMcDonald2013_54-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-HansenMcDonald2013_54-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-HansenMcDonald2013_54-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-HansenMcDonald2013_54-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-HansenMcDonald2013_54-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-HansenMcDonald2013_54-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-HansenMcDonald2013_54-6"><sup><i><b>g</b></i></sup></a> <a href="#cite_ref-HansenMcDonald2013_54-7"><sup><i><b>h</b></i></sup></a> <a href="#cite_ref-HansenMcDonald2013_54-8"><sup><i><b>i</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHansenMcDonald2013" class="citation book cs1">Hansen, Jean-Pierre; McDonald, Ian R. (2013). <i>Theory of simple liquids: with applications to soft matter</i>. Amsterdam. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-12-387033-9" title="Special:BookSources/978-0-12-387033-9"><bdi>978-0-12-387033-9</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/855895733">855895733</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Theory+of+simple+liquids%3A+with+applications+to+soft+matter&rft.place=Amsterdam&rft.date=2013&rft_id=info%3Aoclcnum%2F855895733&rft.isbn=978-0-12-387033-9&rft.aulast=Hansen&rft.aufirst=Jean-Pierre&rft.au=McDonald%2C+Ian+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: location missing publisher (<a href="/wiki/Category:CS1_maint:_location_missing_publisher" title="Category:CS1 maint: location missing publisher">link</a>)</span></span> </li> <li id="cite_note-Kardar_2007_p.-55"><span class="mw-cite-backlink">^ <a href="#cite_ref-Kardar_2007_p._55-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Kardar_2007_p._55-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKardar2007" class="citation book cs1">Kardar, Mehran (2007). <i>Statistical physics of particles</i>. New York, NY: Cambridge University Press. p. 130. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-87342-0" title="Special:BookSources/978-0-521-87342-0"><bdi>978-0-521-87342-0</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/148639922">148639922</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Statistical+physics+of+particles&rft.place=New+York%2C+NY&rft.pages=130&rft.pub=Cambridge+University+Press&rft.date=2007&rft_id=info%3Aoclcnum%2F148639922&rft.isbn=978-0-521-87342-0&rft.aulast=Kardar&rft.aufirst=Mehran&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-Gray1984-56"><span class="mw-cite-backlink">^ <a href="#cite_ref-Gray1984_56-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Gray1984_56-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGrayGubbinsJoslin1984–2011" class="citation book cs1">Gray, C. G.; Gubbins, Keith E.; Joslin, C. G. (1984–2011). <i>Theory of molecular fluids</i>. Oxford: Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-19-855602-0" title="Special:BookSources/0-19-855602-0"><bdi>0-19-855602-0</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/10145548">10145548</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Theory+of+molecular+fluids&rft.place=Oxford&rft.pub=Oxford+University+Press&rft.date=1984%2F2011&rft_id=info%3Aoclcnum%2F10145548&rft.isbn=0-19-855602-0&rft.aulast=Gray&rft.aufirst=C.+G.&rft.au=Gubbins%2C+Keith+E.&rft.au=Joslin%2C+C.+G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-MarxHutter_2012-57"><span class="mw-cite-backlink">^ <a href="#cite_ref-MarxHutter_2012_57-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-MarxHutter_2012_57-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMarxHutter2012" class="citation book cs1">Marx, Dominik; Hutter, Jürg (2012). <i>Ab initio molecular dynamics: basic theory and advanced methods</i>. Cambridge. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-89863-8" title="Special:BookSources/978-0-521-89863-8"><bdi>978-0-521-89863-8</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/869135580">869135580</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Ab+initio+molecular+dynamics%3A+basic+theory+and+advanced+methods&rft.place=Cambridge&rft.date=2012&rft_id=info%3Aoclcnum%2F869135580&rft.isbn=978-0-521-89863-8&rft.aulast=Marx&rft.aufirst=Dominik&rft.au=Hutter%2C+J%C3%BCrg&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: location missing publisher (<a href="/wiki/Category:CS1_maint:_location_missing_publisher" title="Category:CS1 maint: location missing publisher">link</a>)</span></span> </li> <li id="cite_note-58"><span class="mw-cite-backlink"><b><a href="#cite_ref-58">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFisher1964" class="citation cs2">Fisher, I.Z. (1964), <i>Statistical Theory of Liquids</i>, The University of Chicago Press</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Statistical+Theory+of+Liquids&rft.pub=The+University+of+Chicago+Press&rft.date=1964&rft.aulast=Fisher&rft.aufirst=I.Z.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-Ceriotti2013-59"><span class="mw-cite-backlink"><b><a href="#cite_ref-Ceriotti2013_59-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCeriottiCunyParrinelloManolopoulos2013" class="citation journal cs1">Ceriotti, Michele; Cuny, Jérôme; Parrinello, Michele; Manolopoulos, David E. (2013-09-06). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3785726">"Nuclear quantum effects and hydrogen bond fluctuations in water"</a>. <i>Proceedings of the National Academy of Sciences</i>. <b>110</b> (39): 15591–15596. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2013PNAS..11015591C">2013PNAS..11015591C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1073%2Fpnas.1308560110">10.1073/pnas.1308560110</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0027-8424">0027-8424</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3785726">3785726</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/24014589">24014589</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+National+Academy+of+Sciences&rft.atitle=Nuclear+quantum+effects+and+hydrogen+bond+fluctuations+in+water&rft.volume=110&rft.issue=39&rft.pages=15591-15596&rft.date=2013-09-06&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC3785726%23id-name%3DPMC&rft_id=info%3Abibcode%2F2013PNAS..11015591C&rft_id=info%3Apmid%2F24014589&rft_id=info%3Adoi%2F10.1073%2Fpnas.1308560110&rft.issn=0027-8424&rft.aulast=Ceriotti&rft.aufirst=Michele&rft.au=Cuny%2C+J%C3%A9r%C3%B4me&rft.au=Parrinello%2C+Michele&rft.au=Manolopoulos%2C+David+E.&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC3785726&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-Markland_Ceriotti2018-60"><span class="mw-cite-backlink"><b><a href="#cite_ref-Markland_Ceriotti2018_60-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMarklandCeriotti2018" class="citation journal cs1">Markland, Thomas E.; Ceriotti, Michele (2018-02-28). "Nuclear quantum effects enter the mainstream". <i>Nature Reviews Chemistry</i>. <b>2</b> (3). Springer Science and Business Media LLC. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1803.01037">1803.01037</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fs41570-017-0109">10.1038/s41570-017-0109</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/2397-3358">2397-3358</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:4938804">4938804</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature+Reviews+Chemistry&rft.atitle=Nuclear+quantum+effects+enter+the+mainstream&rft.volume=2&rft.issue=3&rft.date=2018-02-28&rft_id=info%3Aarxiv%2F1803.01037&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A4938804%23id-name%3DS2CID&rft.issn=2397-3358&rft_id=info%3Adoi%2F10.1038%2Fs41570-017-0109&rft.aulast=Markland&rft.aufirst=Thomas+E.&rft.au=Ceriotti%2C+Michele&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-Li2011-61"><span class="mw-cite-backlink"><b><a href="#cite_ref-Li2011_61-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLiWalkerMichaelides2011" class="citation journal cs1">Li, Xin-Zheng; Walker, Brent; Michaelides, Angelos (2011-04-04). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3081025">"Quantum nature of the hydrogen bond"</a>. <i>Proceedings of the National Academy of Sciences</i>. <b>108</b> (16): 6369–6373. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2011PNAS..108.6369L">2011PNAS..108.6369L</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1073%2Fpnas.1016653108">10.1073/pnas.1016653108</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0027-8424">0027-8424</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3081025">3081025</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+National+Academy+of+Sciences&rft.atitle=Quantum+nature+of+the+hydrogen+bond&rft.volume=108&rft.issue=16&rft.pages=6369-6373&rft.date=2011-04-04&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC3081025%23id-name%3DPMC&rft.issn=0027-8424&rft_id=info%3Adoi%2F10.1073%2Fpnas.1016653108&rft_id=info%3Abibcode%2F2011PNAS..108.6369L&rft.aulast=Li&rft.aufirst=Xin-Zheng&rft.au=Walker%2C+Brent&rft.au=Michaelides%2C+Angelos&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC3081025&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-62"><span class="mw-cite-backlink"><b><a href="#cite_ref-62">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBorn1940" class="citation journal cs1">Born, Max (1940). "On the stability of crystal lattices". <i><a href="/wiki/Mathematical_Proceedings_of_the_Cambridge_Philosophical_Society" title="Mathematical Proceedings of the Cambridge Philosophical Society">Mathematical Proceedings of the Cambridge Philosophical Society</a></i>. <b>36</b> (2): 160–172. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1940PCPS...36..160B">1940PCPS...36..160B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2FS0305004100017138">10.1017/S0305004100017138</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:104272002">104272002</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mathematical+Proceedings+of+the+Cambridge+Philosophical+Society&rft.atitle=On+the+stability+of+crystal+lattices&rft.volume=36&rft.issue=2&rft.pages=160-172&rft.date=1940&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A104272002%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1017%2FS0305004100017138&rft_id=info%3Abibcode%2F1940PCPS...36..160B&rft.aulast=Born&rft.aufirst=Max&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-63"><span class="mw-cite-backlink"><b><a href="#cite_ref-63">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBorn1939" class="citation journal cs1">Born, Max (1939). <a rel="nofollow" class="external text" href="http://arquivo.pt/wayback/20160515021512/http://jcp.aip.org/resource/1/jcpsa6/v7/i8/p591_s1?isAuthorized=no">"Thermodynamics of Crystals and Melting"</a>. <i>Journal of Chemical Physics</i>. <b>7</b> (8): 591–604. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1939JChPh...7..591B">1939JChPh...7..591B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.1750497">10.1063/1.1750497</a>. Archived from <a rel="nofollow" class="external text" href="http://jcp.aip.org/resource/1/jcpsa6/v7/i8/p591_s1?isAuthorized=no">the original</a> on 2016-05-15.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Chemical+Physics&rft.atitle=Thermodynamics+of+Crystals+and+Melting&rft.volume=7&rft.issue=8&rft.pages=591-604&rft.date=1939&rft_id=info%3Adoi%2F10.1063%2F1.1750497&rft_id=info%3Abibcode%2F1939JChPh...7..591B&rft.aulast=Born&rft.aufirst=Max&rft_id=http%3A%2F%2Fjcp.aip.org%2Fresource%2F1%2Fjcpsa6%2Fv7%2Fi8%2Fp591_s1%3FisAuthorized%3Dno&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-Krüger2016-64"><span class="mw-cite-backlink">^ <a href="#cite_ref-Krüger2016_64-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Krüger2016_64-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Krüger2016_64-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKrügerKusumaatmajaKuzminShardt2016" class="citation book cs1">Krüger, Timm; Kusumaatmaja, Halim; Kuzmin, Alexandr; Shardt, Orest; Silva, Goncalo; Viggen, Erlend Magnus (2016). <i>The lattice Boltzmann method: principles and practice</i>. Switzerland. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-319-44649-3" title="Special:BookSources/978-3-319-44649-3"><bdi>978-3-319-44649-3</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/963198053">963198053</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+lattice+Boltzmann+method%3A+principles+and+practice&rft.place=Switzerland&rft.date=2016&rft_id=info%3Aoclcnum%2F963198053&rft.isbn=978-3-319-44649-3&rft.aulast=Kr%C3%BCger&rft.aufirst=Timm&rft.au=Kusumaatmaja%2C+Halim&rft.au=Kuzmin%2C+Alexandr&rft.au=Shardt%2C+Orest&rft.au=Silva%2C+Goncalo&rft.au=Viggen%2C+Erlend+Magnus&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: location missing publisher (<a href="/wiki/Category:CS1_maint:_location_missing_publisher" title="Category:CS1 maint: location missing publisher">link</a>)</span></span> </li> <li id="cite_note-Steinhauser2022-65"><span class="mw-cite-backlink"><b><a href="#cite_ref-Steinhauser2022_65-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSteinhauser2022" class="citation book cs1">Steinhauser, M. O. (2022). <i>Computational multiscale modeling of fluids and solids: theory and applications</i>. Cham, Switzerland: Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-030-98954-5" title="Special:BookSources/978-3-030-98954-5"><bdi>978-3-030-98954-5</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/1337924123">1337924123</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Computational+multiscale+modeling+of+fluids+and+solids%3A+theory+and+applications&rft.place=Cham%2C+Switzerland&rft.pub=Springer&rft.date=2022&rft_id=info%3Aoclcnum%2F1337924123&rft.isbn=978-3-030-98954-5&rft.aulast=Steinhauser&rft.aufirst=M.+O.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-Poling2001-66"><span class="mw-cite-backlink"><b><a href="#cite_ref-Poling2001_66-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPolingPrausnitzO'Connell2001" class="citation book cs1">Poling, Bruce E.; Prausnitz, J. M.; O'Connell, John P. (2001). <i>The properties of gases and liquids</i>. New York: McGraw-Hill. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-07-011682-2" title="Special:BookSources/0-07-011682-2"><bdi>0-07-011682-2</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/44712950">44712950</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+properties+of+gases+and+liquids&rft.place=New+York&rft.pub=McGraw-Hill&rft.date=2001&rft_id=info%3Aoclcnum%2F44712950&rft.isbn=0-07-011682-2&rft.aulast=Poling&rft.aufirst=Bruce+E.&rft.au=Prausnitz%2C+J.+M.&rft.au=O%27Connell%2C+John+P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-67"><span class="mw-cite-backlink"><b><a href="#cite_ref-67">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBirdStewartLightfoot2007" class="citation book cs1">Bird, R. Byron; Stewart, Warren E.; Lightfoot, Edwin N. (2007). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=L5FnNlIaGfcC"><i>Transport Phenomena</i></a> (2nd ed.). John Wiley & Sons, Inc. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-470-11539-8" title="Special:BookSources/978-0-470-11539-8"><bdi>978-0-470-11539-8</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200302151358/https://books.google.com/books?id=L5FnNlIaGfcC">Archived</a> from the original on 2020-03-02<span class="reference-accessdate">. Retrieved <span class="nowrap">2019-09-18</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Transport+Phenomena&rft.edition=2nd&rft.pub=John+Wiley+%26+Sons%2C+Inc.&rft.date=2007&rft.isbn=978-0-470-11539-8&rft.aulast=Bird&rft.aufirst=R.+Byron&rft.au=Stewart%2C+Warren+E.&rft.au=Lightfoot%2C+Edwin+N.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DL5FnNlIaGfcC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-Span2000-68"><span class="mw-cite-backlink"><b><a href="#cite_ref-Span2000_68-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSpan2000" class="citation book cs1">Span, R. (2000). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=dd410GGw8wUC&pg=PA1"><i>Multiparameter Equations of State: An Accurate Source of Thermodynamic Property Data</i></a>. Engineering online library. Springer. p. 1. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-67311-8" title="Special:BookSources/978-3-540-67311-8"><bdi>978-3-540-67311-8</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">2023-04-01</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Multiparameter+Equations+of+State%3A+An+Accurate+Source+of+Thermodynamic+Property+Data&rft.series=Engineering+online+library&rft.pages=1&rft.pub=Springer&rft.date=2000&rft.isbn=978-3-540-67311-8&rft.aulast=Span&rft.aufirst=R.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Ddd410GGw8wUC%26pg%3DPA1&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-Huber2022-69"><span class="mw-cite-backlink"><b><a href="#cite_ref-Huber2022_69-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHuberLemmonBellMcLinden2022" class="citation journal cs1">Huber, Marcia L.; Lemmon, Eric W.; Bell, Ian H.; McLinden, Mark O. (2022-06-22). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9619405">"The NIST REFPROP Database for Highly Accurate Properties of Industrially Important Fluids"</a>. <i>Industrial & Engineering Chemistry Research</i>. <b>61</b> (42). American Chemical Society (ACS): 15449–15472. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Facs.iecr.2c01427">10.1021/acs.iecr.2c01427</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0888-5885">0888-5885</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9619405">9619405</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/36329835">36329835</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:249968848">249968848</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Industrial+%26+Engineering+Chemistry+Research&rft.atitle=The+NIST+REFPROP+Database+for+Highly+Accurate+Properties+of+Industrially+Important+Fluids&rft.volume=61&rft.issue=42&rft.pages=15449-15472&rft.date=2022-06-22&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC9619405%23id-name%3DPMC&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A249968848%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1021%2Facs.iecr.2c01427&rft.issn=0888-5885&rft_id=info%3Apmid%2F36329835&rft.aulast=Huber&rft.aufirst=Marcia+L.&rft.au=Lemmon%2C+Eric+W.&rft.au=Bell%2C+Ian+H.&rft.au=McLinden%2C+Mark+O.&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC9619405&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-Tillner-Roth1998-70"><span class="mw-cite-backlink"><b><a href="#cite_ref-Tillner-Roth1998_70-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTillner-RothFriend1998" class="citation journal cs1">Tillner-Roth, Reiner; Friend, Daniel G. (1998). "A Helmholtz Free Energy Formulation of the Thermodynamic Properties of the Mixture {Water + Ammonia}". <i>Journal of Physical and Chemical Reference Data</i>. <b>27</b> (1). AIP Publishing: 63–96. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.556015">10.1063/1.556015</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0047-2689">0047-2689</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Physical+and+Chemical+Reference+Data&rft.atitle=A+Helmholtz+Free+Energy+Formulation+of+the+Thermodynamic+Properties+of+the+Mixture+%7BWater+%2B+Ammonia%7D&rft.volume=27&rft.issue=1&rft.pages=63-96&rft.date=1998&rft_id=info%3Adoi%2F10.1063%2F1.556015&rft.issn=0047-2689&rft.aulast=Tillner-Roth&rft.aufirst=Reiner&rft.au=Friend%2C+Daniel+G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-PrincetonCompanion-71"><span class="mw-cite-backlink"><b><a href="#cite_ref-PrincetonCompanion_71-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMoffatt2015" class="citation cs2">Moffatt, H.K. (2015), "Fluid Dynamics", in Nicholas J. Higham; et al. (eds.), <i>The Princeton Companion to Applied Mathematics</i>, Princeton University Press, pp. 467–476</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Fluid+Dynamics&rft.btitle=The+Princeton+Companion+to+Applied+Mathematics&rft.pages=467-476&rft.pub=Princeton+University+Press&rft.date=2015&rft.aulast=Moffatt&rft.aufirst=H.K.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-Wendt2008-72"><span class="mw-cite-backlink"><b><a href="#cite_ref-Wendt2008_72-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWendtAndersonVon_Karman_Institute_for_Fluid_Dynamics2008" class="citation book cs1">Wendt, John F.; Anderson, John D. Jr.; Von Karman Institute for Fluid Dynamics (2008). <i>Computational fluid dynamics: an introduction</i>. Berlin: Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-85056-4" title="Special:BookSources/978-3-540-85056-4"><bdi>978-3-540-85056-4</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/656397653">656397653</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Computational+fluid+dynamics%3A+an+introduction&rft.place=Berlin&rft.pub=Springer&rft.date=2008&rft_id=info%3Aoclcnum%2F656397653&rft.isbn=978-3-540-85056-4&rft.aulast=Wendt&rft.aufirst=John+F.&rft.au=Anderson%2C+John+D.+Jr.&rft.au=Von+Karman+Institute+for+Fluid+Dynamics&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-Pozrikidis2011-73"><span class="mw-cite-backlink"><b><a href="#cite_ref-Pozrikidis2011_73-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPozrikidis2011" class="citation book cs1">Pozrikidis, C. (2011). <i>Introduction to theoretical and computational fluid dynamics</i>. New York: Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-990912-4" title="Special:BookSources/978-0-19-990912-4"><bdi>978-0-19-990912-4</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/812917029">812917029</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+theoretical+and+computational+fluid+dynamics&rft.place=New+York&rft.pub=Oxford+University+Press&rft.date=2011&rft_id=info%3Aoclcnum%2F812917029&rft.isbn=978-0-19-990912-4&rft.aulast=Pozrikidis&rft.aufirst=C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-Monaghan2005-74"><span class="mw-cite-backlink"><b><a href="#cite_ref-Monaghan2005_74-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMonaghan2005" class="citation journal cs1">Monaghan, J J (2005-07-05). "Smoothed particle hydrodynamics". <i>Reports on Progress in Physics</i>. <b>68</b> (8). IOP Publishing: 1703–1759. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2005RPPh...68.1703M">2005RPPh...68.1703M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F0034-4885%2F68%2F8%2Fr01">10.1088/0034-4885/68/8/r01</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0034-4885">0034-4885</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:5987481">5987481</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Reports+on+Progress+in+Physics&rft.atitle=Smoothed+particle+hydrodynamics&rft.volume=68&rft.issue=8&rft.pages=1703-1759&rft.date=2005-07-05&rft_id=info%3Adoi%2F10.1088%2F0034-4885%2F68%2F8%2Fr01&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A5987481%23id-name%3DS2CID&rft.issn=0034-4885&rft_id=info%3Abibcode%2F2005RPPh...68.1703M&rft.aulast=Monaghan&rft.aufirst=J+J&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-Lind2020-75"><span class="mw-cite-backlink"><b><a href="#cite_ref-Lind2020_75-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLindRogersStansby2020" class="citation journal cs1">Lind, Steven J.; Rogers, Benedict D.; Stansby, Peter K. (2020). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7544338">"Review of smoothed particle hydrodynamics: towards converged Lagrangian flow modelling"</a>. <i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>. <b>476</b> (2241). The Royal Society. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2020RSPSA.47690801L">2020RSPSA.47690801L</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frspa.2019.0801">10.1098/rspa.2019.0801</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1364-5021">1364-5021</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7544338">7544338</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/33071565">33071565</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:221538477">221538477</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+Royal+Society+A%3A+Mathematical%2C+Physical+and+Engineering+Sciences&rft.atitle=Review+of+smoothed+particle+hydrodynamics%3A+towards+converged+Lagrangian+flow+modelling&rft.volume=476&rft.issue=2241&rft.date=2020&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC7544338%23id-name%3DPMC&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A221538477%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2020RSPSA.47690801L&rft.issn=1364-5021&rft_id=info%3Adoi%2F10.1098%2Frspa.2019.0801&rft_id=info%3Apmid%2F33071565&rft.aulast=Lind&rft.aufirst=Steven+J.&rft.au=Rogers%2C+Benedict+D.&rft.au=Stansby%2C+Peter+K.&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC7544338&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-Español2017-76"><span class="mw-cite-backlink"><b><a href="#cite_ref-Español2017_76-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEspañolWarren2017" class="citation journal cs1">Español, Pep; Warren, Patrick B. (2017-04-21). "Perspective: Dissipative particle dynamics". <i>The Journal of Chemical Physics</i>. <b>146</b> (15). AIP Publishing: 150901. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1612.04574">1612.04574</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2017JChPh.146o0901E">2017JChPh.146o0901E</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.4979514">10.1063/1.4979514</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0021-9606">0021-9606</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/28433024">28433024</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:961922">961922</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Journal+of+Chemical+Physics&rft.atitle=Perspective%3A+Dissipative+particle+dynamics&rft.volume=146&rft.issue=15&rft.pages=150901&rft.date=2017-04-21&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A961922%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2017JChPh.146o0901E&rft_id=info%3Aarxiv%2F1612.04574&rft.issn=0021-9606&rft_id=info%3Adoi%2F10.1063%2F1.4979514&rft_id=info%3Apmid%2F28433024&rft.aulast=Espa%C3%B1ol&rft.aufirst=Pep&rft.au=Warren%2C+Patrick+B.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALiquid" class="Z3988"></span></span> </li> <li id="cite_note-Gompper2008-77"><span class="mw-cite-backlink"><b><a href="#cite_ref-Gompper2008_77-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGompperIhleKrollWinkler2009" class="citation book cs1">Gompper, G.; Ihle, T.; Kroll, D. M.; Winkler, R. G. (2009). "Multi-Particle Collision Dynamics: A Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids". <i>Advanced Computer Simulation Approaches for Soft Matter Sciences III</i>. Berlin, Heidelberg: Springer Berlin Heidelberg. pp. 1–87. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/0808.2157">0808.2157</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-540-87706-6_1">10.1007/978-3-540-87706-6_1</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-87705-9" title="Special:BookSources/978-3-540-87705-9"><bdi>978-3-540-87705-9</bdi></a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:8433369">8433369</a>.</cite><span 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.mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="States_of_matter_(list)" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:States_of_matter" title="Template:States of matter"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:States_of_matter" title="Template talk:States of matter"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:States_of_matter" title="Special:EditPage/Template:States of matter"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="States_of_matter_(list)" style="font-size:114%;margin:0 4em"><a href="/wiki/State_of_matter" title="State of matter">States of matter</a> (<a href="/wiki/List_of_states_of_matter" title="List of states of matter">list</a>)</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">State</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Solid" title="Solid">Solid</a></li> <li><a class="mw-selflink selflink">Liquid</a></li> <li><a href="/wiki/Gas" title="Gas">Gas</a> / <a href="/wiki/Vapor" title="Vapor">Vapor</a></li> <li><a href="/wiki/Supercritical_fluid" title="Supercritical fluid">Supercritical fluid</a></li> <li><a href="/wiki/Plasma_(physics)" title="Plasma (physics)">Plasma</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="7" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:Phase_change_-_en.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Phase_change_-_en.svg/150px-Phase_change_-_en.svg.png" decoding="async" width="150" height="159" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Phase_change_-_en.svg/225px-Phase_change_-_en.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Phase_change_-_en.svg/300px-Phase_change_-_en.svg.png 2x" data-file-width="493" data-file-height="524" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Low energy</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bose%E2%80%93Einstein_condensate" title="Bose–Einstein condensate">Bose–Einstein condensate</a></li> <li><a href="/wiki/Fermionic_condensate" title="Fermionic condensate">Fermionic condensate</a></li> <li><a href="/wiki/Degenerate_matter" title="Degenerate matter">Degenerate matter</a></li> <li><a href="/wiki/Quantum_Hall_effect" title="Quantum Hall effect">Quantum Hall</a></li> <li><a href="/wiki/Rydberg_matter" title="Rydberg matter">Rydberg matter</a></li> <li><a href="/wiki/Strange_matter" title="Strange matter">Strange matter</a></li> <li><a href="/wiki/Superfluidity" title="Superfluidity">Superfluid</a></li> <li><a href="/wiki/Supersolid" title="Supersolid">Supersolid</a></li> <li><a href="/wiki/Photonic_molecule" title="Photonic molecule">Photonic molecule</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">High energy</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/QCD_matter" title="QCD matter">QCD matter</a></li> <li><a href="/wiki/Quark%E2%80%93gluon_plasma" title="Quark–gluon plasma">Quark–gluon plasma</a></li> <li><a href="/wiki/Color-glass_condensate" title="Color-glass condensate">Color-glass condensate</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other states</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Colloid" title="Colloid">Colloid</a></li> <li><a href="/wiki/Crystal" title="Crystal">Crystal</a></li> <li><a href="/wiki/Liquid_crystal" title="Liquid crystal">Liquid crystal</a></li> <li><a href="/wiki/Time_crystal" title="Time crystal">Time crystal</a></li> <li><a href="/wiki/Quantum_spin_liquid" title="Quantum spin liquid">Quantum spin liquid</a></li> <li><a href="/wiki/Exotic_matter" title="Exotic matter">Exotic matter</a></li> <li><a href="/wiki/Programmable_matter" title="Programmable matter">Programmable matter</a></li> <li><a href="/wiki/Dark_matter" title="Dark matter">Dark matter</a></li> <li><a href="/wiki/Antimatter" title="Antimatter">Antimatter</a></li> <li>Magnetically ordered <ul><li><a href="/wiki/Antiferromagnetism" title="Antiferromagnetism">Antiferromagnet</a></li> <li><a href="/wiki/Ferrimagnetism" title="Ferrimagnetism">Ferrimagnet</a></li> <li><a href="/wiki/Ferromagnetism" title="Ferromagnetism">Ferromagnet</a></li></ul></li> <li><a href="/wiki/String-net_liquid" title="String-net liquid">String-net liquid</a></li> <li><a href="/wiki/Superglass" title="Superglass">Superglass</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Phase_transitions" class="mw-redirect" title="Phase transitions">Phase transitions</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Boiling" title="Boiling">Boiling</a></li> <li><a href="/wiki/Boiling_point" title="Boiling point">Boiling point</a></li> <li><a href="/wiki/Condensation" title="Condensation">Condensation</a></li> <li><a href="/wiki/Critical_line_(thermodynamics)" title="Critical line (thermodynamics)">Critical line</a></li> <li><a href="/wiki/Critical_point_(thermodynamics)" title="Critical point (thermodynamics)">Critical point</a></li> <li><a href="/wiki/Crystallization" title="Crystallization">Crystallization</a></li> <li><a href="/wiki/Deposition_(phase_transition)" title="Deposition (phase transition)">Deposition</a></li> <li><a href="/wiki/Evaporation" title="Evaporation">Evaporation</a></li> <li><a href="/wiki/Flash_evaporation" title="Flash evaporation">Flash evaporation</a></li> <li><a href="/wiki/Freezing" title="Freezing">Freezing</a></li> <li><a href="/wiki/Chemical_ionization" title="Chemical ionization">Chemical ionization</a></li> <li><a href="/wiki/Ionization" title="Ionization">Ionization</a></li> <li><a href="/wiki/Lambda_point" title="Lambda point">Lambda point</a></li> <li><a href="/wiki/Melting" title="Melting">Melting</a></li> <li><a href="/wiki/Melting_point" title="Melting point">Melting point</a></li> <li><a href="/wiki/Plasma_recombination" title="Plasma recombination">Recombination</a></li> <li><a href="/wiki/Regelation" title="Regelation">Regelation</a></li> <li><a href="/wiki/Vapor%E2%80%93liquid_equilibrium" title="Vapor–liquid equilibrium">Saturated fluid</a></li> <li><a href="/wiki/Sublimation_(phase_transition)" title="Sublimation (phase transition)">Sublimation</a></li> <li><a href="/wiki/Supercooling" title="Supercooling">Supercooling</a></li> <li><a href="/wiki/Triple_point" title="Triple point">Triple point</a></li> <li><a href="/wiki/Vaporization" title="Vaporization">Vaporization</a></li> <li><a href="/wiki/Vitrification" title="Vitrification">Vitrification</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Quantities</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Enthalpy_of_fusion" title="Enthalpy of fusion">Enthalpy of fusion</a></li> <li><a href="/wiki/Enthalpy_of_sublimation" title="Enthalpy of sublimation">Enthalpy of sublimation</a></li> <li><a href="/wiki/Enthalpy_of_vaporization" title="Enthalpy of vaporization">Enthalpy of vaporization</a></li> <li><a href="/wiki/Latent_heat" title="Latent heat">Latent heat</a></li> <li><a href="/wiki/Latent_internal_energy" title="Latent internal energy">Latent internal energy</a></li> <li><a href="/wiki/Trouton%27s_rule" title="Trouton's rule">Trouton's rule</a></li> <li><a href="/wiki/Volatility_(chemistry)" title="Volatility (chemistry)">Volatility</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Baryonic_matter" class="mw-redirect" title="Baryonic matter">Baryonic matter</a></li> <li><a href="/wiki/Binodal" title="Binodal">Binodal</a></li> <li><a href="/wiki/Compressed_fluid" title="Compressed fluid">Compressed fluid</a></li> <li><a href="/wiki/Cooling_curve" title="Cooling curve">Cooling curve</a></li> <li><a href="/wiki/Equation_of_state" title="Equation of state">Equation of state</a></li> <li><a href="/wiki/Leidenfrost_effect" title="Leidenfrost effect">Leidenfrost effect</a></li> <li><a href="/wiki/Macroscopic_quantum_phenomena" title="Macroscopic quantum phenomena">Macroscopic quantum phenomena</a></li> <li><a href="/wiki/Mpemba_effect" title="Mpemba effect">Mpemba effect</a></li> <li><a href="/wiki/Order_and_disorder_(physics)" class="mw-redirect" title="Order and disorder (physics)">Order and disorder (physics)</a></li> <li><a href="/wiki/Spinodal" title="Spinodal">Spinodal</a></li> <li><a href="/wiki/Superconductivity" title="Superconductivity">Superconductivity</a></li> <li><a href="/wiki/Superheated_water" title="Superheated water">Superheated vapor</a></li> <li><a href="/wiki/Superheating" title="Superheating">Superheating</a></li> <li><a href="/wiki/Thermo-dielectric_effect" title="Thermo-dielectric effect">Thermo-dielectric effect</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"><style data-mw-deduplicate="TemplateStyles:r1038841319">.mw-parser-output .tooltip-dotted{border-bottom:1px dotted;cursor:help}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1038841319"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1038841319"></div><div role="navigation" class="navbox authority-control" aria-label="Navbox" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a>: National <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q11435#identifiers" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span 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