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id="toc-Deborah_number-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Reynolds_number" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Reynolds_number"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Reynolds number</span> </div> </a> <ul id="toc-Reynolds_number-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Measurement" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Measurement"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Measurement</span> </div> </a> <ul id="toc-Measurement-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Applications" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Applications"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</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-Materials_science" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Materials_science"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Materials science</span> </div> </a> <ul id="toc-Materials_science-sublist" class="vector-toc-list"> <li id="toc-Polymers" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Polymers"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1.1</span> <span>Polymers</span> </div> </a> <ul id="toc-Polymers-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Biopolymers" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Biopolymers"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1.2</span> <span>Biopolymers</span> </div> </a> <ul id="toc-Biopolymers-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sol-gel" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Sol-gel"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1.3</span> <span>Sol-gel</span> </div> </a> <ul id="toc-Sol-gel-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Geophysics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Geophysics"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Geophysics</span> </div> </a> <ul id="toc-Geophysics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Physiology" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Physiology"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Physiology</span> </div> </a> <ul id="toc-Physiology-sublist" class="vector-toc-list"> <li id="toc-Red_blood_cell_aggregation" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Red_blood_cell_aggregation"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3.1</span> <span>Red blood cell aggregation</span> </div> </a> <ul id="toc-Red_blood_cell_aggregation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Disease_and_diagnostics" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Disease_and_diagnostics"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3.2</span> <span>Disease and diagnostics</span> </div> </a> <ul id="toc-Disease_and_diagnostics-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Zoology" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Zoology"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.4</span> <span>Zoology</span> </div> </a> <ul id="toc-Zoology-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Food_rheology" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Food_rheology"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.5</span> <span>Food rheology</span> </div> </a> <ul id="toc-Food_rheology-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Concrete_rheology" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Concrete_rheology"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.6</span> <span>Concrete rheology</span> </div> </a> <ul id="toc-Concrete_rheology-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Filled_polymer_rheology" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Filled_polymer_rheology"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.7</span> <span>Filled polymer rheology</span> </div> </a> <ul id="toc-Filled_polymer_rheology-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Rheologist" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Rheologist"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Rheologist</span> </div> </a> <ul id="toc-Rheologist-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</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 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>External links</span> </div> </a> <ul id="toc-External_links-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">Rheology</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" 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Available in 46 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-46" 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">46 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B9%D9%84%D9%85_%D8%A7%D9%84%D8%AC%D8%B1%D9%8A%D8%A7%D9%86" title="علم الجريان – Arabic" lang="ar" hreflang="ar" data-title="علم الجريان" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Reolog%C3%ADa" title="Reología – Asturian" lang="ast" hreflang="ast" data-title="Reología" 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/Reologiya" title="Reologiya – Azerbaijani" lang="az" hreflang="az" data-title="Reologiya" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A0%D0%B5%D0%BE%D0%BB%D0%BE%D0%B3%D0%B8%D1%8F" title="Реология – Bulgarian" lang="bg" hreflang="bg" data-title="Реология" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Reologia" title="Reologia – Catalan" lang="ca" hreflang="ca" data-title="Reologia" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Reologie" title="Reologie – Czech" lang="cs" hreflang="cs" data-title="Reologie" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Rheologie" title="Rheologie – German" lang="de" hreflang="de" data-title="Rheologie" 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/Reoloogia" title="Reoloogia – Estonian" lang="et" hreflang="et" data-title="Reoloogia" 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%A1%CE%B5%CE%BF%CE%BB%CE%BF%CE%B3%CE%AF%CE%B1" title="Ρεολογία – Greek" lang="el" hreflang="el" data-title="Ρεολογία" 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/Reolog%C3%ADa" title="Reología – Spanish" lang="es" hreflang="es" data-title="Reología" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Erreologia" title="Erreologia – Basque" lang="eu" hreflang="eu" data-title="Erreologia" 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/%D8%B1%D8%A6%D9%88%D9%84%D9%88%DA%98%DB%8C" title="رئولوژی – Persian" lang="fa" hreflang="fa" data-title="رئولوژی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Rh%C3%A9ologie" title="Rhéologie – French" lang="fr" hreflang="fr" data-title="Rhéologie" 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/R%C3%A9a-eola%C3%ADocht" title="Réa-eolaíocht – Irish" lang="ga" hreflang="ga" data-title="Réa-eolaíocht" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Reolox%C3%ADa" title="Reoloxía – Galician" lang="gl" hreflang="gl" data-title="Reoloxía" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9C%A0%EB%B3%80%ED%95%99" title="유변학 – Korean" lang="ko" hreflang="ko" data-title="유변학" 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%8C%D5%A5%D5%B8%D5%AC%D5%B8%D5%A3%D5%AB%D5%A1" title="Ռեոլոգիա – Armenian" lang="hy" hreflang="hy" data-title="Ռեոլոգիա" 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%AA%E0%A5%8D%E0%A4%B0%E0%A4%B5%E0%A4%BE%E0%A4%B9%E0%A4%BF%E0%A4%95%E0%A5%80" title="प्रवाहिकी – Hindi" lang="hi" hreflang="hi" data-title="प्रवाहिकी" 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/Reologija" title="Reologija – Croatian" lang="hr" hreflang="hr" data-title="Reologija" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Reologi" title="Reologi – Indonesian" lang="id" hreflang="id" data-title="Reologi" 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-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Flotfr%C3%A6%C3%B0i" title="Flotfræði – Icelandic" lang="is" hreflang="is" data-title="Flotfræði" 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/Reologia" title="Reologia – Italian" lang="it" hreflang="it" data-title="Reologia" 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%A8%D7%90%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94" title="ראולוגיה – Hebrew" lang="he" hreflang="he" data-title="ראולוגיה" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A0%D0%B5%D0%BE%D0%BB%D0%BE%D0%B3%D0%B8%D1%8F" title="Реология – Kazakh" lang="kk" hreflang="kk" data-title="Реология" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%A0%D0%B5%D0%BE%D0%BB%D0%BE%D0%B3%D0%B8%D1%8F" title="Реология – Kyrgyz" lang="ky" hreflang="ky" data-title="Реология" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Reologija" title="Reologija – Lithuanian" lang="lt" hreflang="lt" data-title="Reologija" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Reol%C3%B3gia" title="Reológia – Hungarian" lang="hu" hreflang="hu" data-title="Reológia" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Reologie" title="Reologie – Dutch" lang="nl" hreflang="nl" data-title="Reologie" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%AC%E3%82%AA%E3%83%AD%E3%82%B8%E3%83%BC" title="レオロジー – Japanese" lang="ja" hreflang="ja" data-title="レオロジー" 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-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Reologi" title="Reologi – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Reologi" 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-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Reologiya" title="Reologiya – Uzbek" lang="uz" hreflang="uz" data-title="Reologiya" 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-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Reologia" title="Reologia – Polish" lang="pl" hreflang="pl" data-title="Reologia" 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/Reologia" title="Reologia – Portuguese" lang="pt" hreflang="pt" data-title="Reologia" 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/Reologie" title="Reologie – Romanian" lang="ro" hreflang="ro" data-title="Reologie" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A0%D0%B5%D0%BE%D0%BB%D0%BE%D0%B3%D0%B8%D1%8F" title="Реология – Russian" lang="ru" hreflang="ru" data-title="Реология" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B7%83%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B7%90%E0%B6%AD%E0%B7%92_%E0%B7%80%E0%B7%92%E0%B6%AF%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B7%8F%E0%B7%80" title="ස්‍රැති විද්‍යාව – Sinhala" lang="si" hreflang="si" data-title="ස්‍රැති විද්‍යාව" 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/Rheology" title="Rheology – Simple English" lang="en-simple" hreflang="en-simple" data-title="Rheology" 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-sk mw-list-item"><a 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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 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/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 href="/wiki/Liquid" title="Liquid">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"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a class="mw-selflink selflink">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><b>Rheology</b> (<span class="rt-commentedText nowrap"><span class="IPA nopopups noexcerpt" lang="en-fonipa"><a href="/wiki/Help:IPA/English" title="Help:IPA/English">/<span style="border-bottom:1px dotted"><span title="'r' in 'rye'">r</span><span title="/iː/: 'ee' in 'fleece'">iː</span><span title="/ˈ/: primary stress follows">ˈ</span><span title="/ɒ/: 'o' in 'body'">ɒ</span><span title="'l' in 'lie'">l</span><span title="/ə/: 'a' in 'about'">ə</span><span title="/dʒ/: 'j' in 'jam'">dʒ</span><span title="/i/: 'y' in 'happy'">i</span></span>/</a></span></span>; from <a href="/wiki/Greek_language" title="Greek language">Greek</a> <i> </i>ῥέω<i> (rhéō)</i> 'flow' and <i> </i>-λoγία<i> (-logia)</i> 'study of') is the study of the flow of <a href="/wiki/Matter" title="Matter">matter</a>, primarily in a <a href="/wiki/Fluid" title="Fluid">fluid</a> (<a href="/wiki/Liquid" title="Liquid">liquid</a> or <a href="/wiki/Gas" title="Gas">gas</a>) state but also as "soft <a href="/wiki/Solid" title="Solid">solids</a>" or solids under conditions in which they respond with <a href="/wiki/Plasticity_(physics)" title="Plasticity (physics)">plastic</a> flow rather than deforming <a href="/wiki/Elasticity_(physics)" title="Elasticity (physics)">elastically</a> in response to an applied force.<a rel="nofollow" class="external autonumber" href="https://books.google.com/books?id=B1e0uxFg4oYC&dq=rheology&pg=PA1">[1]</a> Rheology is the branch of <a href="/wiki/Physics" title="Physics">physics</a> that deals with the <a href="/wiki/Deformation_(physics)" title="Deformation (physics)">deformation</a> and flow of materials, both solids and liquids.<sup id="cite_ref-Schowalter_1-0" class="reference"><a href="#cite_note-Schowalter-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>The term <i><a href="https://en.wiktionary.org/wiki/rheology" class="extiw" title="wikt:rheology">rheology</a></i> was coined by <a href="/wiki/Eugene_C._Bingham" title="Eugene C. Bingham">Eugene C. Bingham</a>, a professor at <a href="/wiki/Lafayette_College" title="Lafayette College">Lafayette College</a>, in 1920 from a suggestion by a colleague, <a href="/wiki/Markus_Reiner" title="Markus Reiner">Markus Reiner</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-deb1_3-0" class="reference"><a href="#cite_note-deb1-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> The term was inspired by the <a href="/wiki/Aphorism" title="Aphorism">aphorism</a> of <a href="/wiki/Heraclitus" title="Heraclitus">Heraclitus</a> (often mistakenly attributed to <a href="/wiki/Simplicius_of_Cilicia" title="Simplicius of Cilicia">Simplicius</a>), <span title="Ancient Greek (to 1453)-language text"><i lang="grc-Latn"><a href="/wiki/Heraclitus#Panta_rhei,_"everything_flows"" title="Heraclitus">panta rhei</a></i></span> (<span title="Ancient Greek (to 1453)-language text"><span lang="grc">πάντα ῥεῖ</span></span>, 'everything flows'<sup id="cite_ref-Barnes1982_4-0" class="reference"><a href="#cite_note-Barnes1982-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>) and was first used to describe the flow of liquids and the deformation of solids. It applies to substances that have a complex microstructure, such as <a href="/wiki/Mud" title="Mud">muds</a>, <a href="/wiki/Sludge" title="Sludge">sludges</a>, <a href="/wiki/Suspension_(chemistry)" title="Suspension (chemistry)">suspensions</a>, and <a href="/wiki/Polymer" title="Polymer">polymers</a> and other <a href="/wiki/Glass_transition" title="Glass transition">glass formers</a> (e.g., silicates), as well as many foods and additives, <a href="/wiki/Bodily_fluid" class="mw-redirect" title="Bodily fluid">bodily fluids</a> (e.g., blood) and other <a href="/wiki/Body_fluid" title="Body fluid">biological materials</a>, and other materials that belong to the class of <a href="/wiki/Soft_matter" title="Soft matter">soft matter</a> such as food. </p><p><a href="/wiki/Newtonian_fluids" class="mw-redirect" title="Newtonian fluids">Newtonian fluids</a> can be characterized by a single coefficient of <a href="/wiki/Viscosity" title="Viscosity">viscosity</a> for a specific temperature. Although this viscosity will change with temperature, it does not change with the <a href="/wiki/Strain_rate" title="Strain rate">strain rate</a>. Only a small group of fluids exhibit such constant viscosity. The large class of fluids whose viscosity changes with the strain rate (the relative <a href="/wiki/Flow_velocity" title="Flow velocity">flow velocity</a>) are called <a href="/wiki/Non-Newtonian_fluids" class="mw-redirect" title="Non-Newtonian fluids">non-Newtonian fluids</a>. </p><p>Rheology generally accounts for the behavior of non-Newtonian fluids by characterizing the minimum number of functions that are needed to relate stresses with rate of change of strain or strain rates. For example, <a href="/wiki/Ketchup" title="Ketchup">ketchup</a> can have its <a href="/wiki/Viscosity" title="Viscosity">viscosity</a> reduced by shaking (or other forms of mechanical agitation, where the relative movement of different layers in the material actually causes the reduction in viscosity), but water cannot. Ketchup is a shear-thinning material, like <a href="/wiki/Yogurt" title="Yogurt">yogurt</a> and <a href="/wiki/Emulsion" title="Emulsion">emulsion</a> <a href="/wiki/Paint" title="Paint">paint</a> (US terminology <a href="/wiki/Latex_paint" class="mw-redirect" title="Latex paint">latex paint</a> or <a href="/wiki/Acrylic_paint" title="Acrylic paint">acrylic paint</a>), exhibiting <a href="/wiki/Thixotropy" title="Thixotropy">thixotropy</a>, where an increase in relative flow velocity will cause a reduction in viscosity, for example, by stirring. Some other non-Newtonian materials show the opposite behavior, <a href="/wiki/Rheopecty" title="Rheopecty">rheopecty</a> (viscosity increasing with relative deformation), and are called shear-thickening or <a href="/wiki/Dilatant" title="Dilatant">dilatant</a> materials. Since Sir <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a> originated the concept of viscosity, the study of liquids with strain-rate-dependent viscosity is also often called <i><a href="/wiki/Non-Newtonian_fluid" title="Non-Newtonian fluid">Non-Newtonian fluid mechanics</a></i>.<sup id="cite_ref-Schowalter_1-1" class="reference"><a href="#cite_note-Schowalter-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>The experimental characterisation of a material's rheological behaviour is known as <i><a href="/wiki/Rheometry" title="Rheometry">rheometry</a></i>, although the term <i>rheology</i> is frequently used synonymously with rheometry, particularly by experimentalists. Theoretical aspects of rheology are the relation of the flow/deformation behaviour of material and its internal structure (e.g., the orientation and elongation of polymer molecules) and the flow/deformation behaviour of materials that cannot be described by classical fluid mechanics or elasticity. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Scope">Scope</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rheology&action=edit&section=1" title="Edit section: Scope"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In practice, rheology is principally concerned with extending <a href="/wiki/Continuum_mechanics" title="Continuum mechanics">continuum mechanics</a> to characterize the flow of materials that exhibit a combination of <a href="/wiki/Elastic_deformation" class="mw-redirect" title="Elastic deformation">elastic</a>, <a href="/wiki/Viscosity" title="Viscosity">viscous</a> and <a href="/wiki/Plastic" title="Plastic">plastic</a> behavior by properly combining <a href="/wiki/Theory_of_elasticity" class="mw-redirect" title="Theory of elasticity">elasticity</a> and (<a href="/wiki/Newtonian_fluid" title="Newtonian fluid">Newtonian</a>) <a href="/wiki/Fluid_mechanics" title="Fluid mechanics">fluid mechanics</a>. It is also concerned with predicting mechanical behavior (on the continuum mechanical scale) based on the micro- or nanostructure of the material, e.g. the <a href="/wiki/Molecule" title="Molecule">molecular</a> size and architecture of <a href="/wiki/Polymer" title="Polymer">polymers</a> in solution or the particle size distribution in a solid suspension. Materials with the characteristics of a fluid will flow when subjected to a <a href="/wiki/Stress_(physics)" class="mw-redirect" title="Stress (physics)">stress</a>, which is defined as the force per area. There are different sorts of stress (e.g. shear, torsional, etc.), and materials can respond differently under different stresses. Much of theoretical rheology is concerned with associating external forces and torques with internal stresses, internal strain gradients, and flow velocities.<sup id="cite_ref-Schowalter_1-2" class="reference"><a href="#cite_note-Schowalter-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-bird1_6-0" class="reference"><a href="#cite_note-bird1-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-bird2_7-0" class="reference"><a href="#cite_note-bird2-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-morris1_8-0" class="reference"><a href="#cite_note-morris1-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <table class="wikitable"> <tbody><tr> <td rowspan="4"><a href="/wiki/Continuum_mechanics" title="Continuum mechanics">Continuum mechanics</a><br /><small>The study of the physics of continuous materials</small> </td> <td rowspan="2"><a href="/wiki/Solid_mechanics" title="Solid mechanics">Solid mechanics</a><br /><small>The study of the physics of continuous materials with a defined rest shape.</small> </td> <td colspan="2"><a href="/wiki/Elasticity_(physics)" title="Elasticity (physics)">Elasticity</a><br /><small>Describes materials that return to their rest shape after applied <a href="/wiki/Stress_(physics)" class="mw-redirect" title="Stress (physics)">stresses</a> are removed.</small> </td></tr> <tr> <td><a href="/wiki/Plasticity_(physics)" title="Plasticity (physics)">Plasticity</a><br /><small>Describes materials that permanently deform after a sufficient applied stress.</small> </td> <td rowspan="2"><b>Rheology</b><br /><small>The study of materials with both solid and fluid characteristics.</small> </td></tr> <tr> <td rowspan="2"><a href="/wiki/Fluid_mechanics" title="Fluid mechanics">Fluid mechanics</a><br /><small>The study of the physics of continuous materials which deform when subjected to a force.</small> </td> <td><a href="/wiki/Non-Newtonian_fluid" title="Non-Newtonian fluid">Non-Newtonian fluid</a><br /><small>Do not undergo strain rates proportional to the applied shear stress.</small> </td></tr> <tr> <td colspan="2"><a href="/wiki/Newtonian_fluid" title="Newtonian fluid">Newtonian fluids</a> undergo strain rates proportional to the applied shear stress. </td></tr></tbody></table> <p>Rheology unites the seemingly unrelated fields of <a href="/wiki/Plasticity_(physics)" title="Plasticity (physics)">plasticity</a> and <a href="/wiki/Non-Newtonian_fluid" title="Non-Newtonian fluid">non-Newtonian fluid</a> dynamics by recognizing that materials undergoing these types of deformation are unable to support a stress (particularly a <a href="/wiki/Shear_stress" title="Shear stress">shear stress</a>, since it is easier to analyze shear deformation) in static <a href="/wiki/Mechanical_equilibrium" title="Mechanical equilibrium">equilibrium</a>. In this sense, a solid undergoing plastic <a href="/wiki/Deformation_(mechanics)" class="mw-redirect" title="Deformation (mechanics)">deformation</a> is a <a href="/wiki/Fluid" title="Fluid">fluid</a>, although no viscosity coefficient is associated with this flow. Granular rheology refers to the continuum mechanical description of <a href="/wiki/Granular_material" title="Granular material">granular materials</a>. </p><p>One of the major tasks of rheology is to establish by measurement the relationships between <a href="/wiki/Strain_(materials_science)" class="mw-redirect" title="Strain (materials science)">strains</a> (or rates of strain) and stresses, although a number of theoretical developments (such as assuring frame invariants) are also required before using the empirical data. These experimental techniques are known as <a href="/wiki/Rheometry" title="Rheometry">rheometry</a> and are concerned with the determination of well-defined <i>rheological material functions</i>. Such relationships are then amenable to mathematical treatment by the established methods of <a href="/wiki/Continuum_mechanics" title="Continuum mechanics">continuum mechanics</a>. </p><p>The characterization of flow or deformation originating from a simple shear stress field is called <b>shear rheometry</b> (or shear rheology). The study of extensional flows is called <b>extensional rheology</b>. Shear flows are much easier to study and thus much more experimental data are available for shear flows than for extensional flows. </p> <div class="mw-heading mw-heading2"><h2 id="Viscoelasticity">Viscoelasticity</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rheology&action=edit&section=2" title="Edit section: Viscoelasticity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Viscoelasticity" title="Viscoelasticity">Viscoelasticity</a></div> <ul><li>Fluid and solid character are relevant at long times:<br />We consider the application of a constant stress (a so-called <i>creep experiment</i>): <ul><li>if the material, after some deformation, eventually resists further deformation, it is considered a solid</li> <li>if, by contrast, the material flows indefinitely, it is considered a fluid</li></ul></li> <li>By contrast, <i>elastic and viscous</i> (or intermediate, <a href="/wiki/Viscoelastic" class="mw-redirect" title="Viscoelastic">viscoelastic</a>) behaviour is relevant at short times (<i>transient behaviour</i>):<br />We again consider the application of a constant stress:<sup id="cite_ref-creep1_9-0" class="reference"><a href="#cite_note-creep1-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> <ul><li>if the material deformation strain increases linearly with increasing applied stress, then the material is linear elastic within the range it shows recoverable strains. Elasticity is essentially a time independent processes, as the strains appear the moment the stress is applied, without any time delay.</li> <li>if the material deformation strain rate increases linearly with increasing applied stress, then the material is viscous in the Newtonian sense. These materials are characterized due to the time delay between the applied constant stress and the maximum strain.</li> <li>if the materials behaves as a combination of viscous and elastic components, then the material is viscoelastic. Theoretically such materials can show both instantaneous deformation as elastic material and a delayed time dependent deformation as in fluids.</li></ul></li> <li><a href="/wiki/Plasticity_(physics)" title="Plasticity (physics)">Plasticity</a> is the behavior observed after the material is subjected to a <i>yield stress</i>:<br />A material that behaves as a solid under low applied stresses may start to flow above a certain level of stress, called the <i><a href="/wiki/Yield_stress" class="mw-redirect" title="Yield stress">yield stress</a></i> of the material. The term <i>plastic solid</i> is often used when this plasticity threshold is rather high, while <i>yield stress fluid</i> is used when the threshold stress is rather low. However, there is no fundamental difference between the two concepts.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Dimensionless_numbers">Dimensionless numbers</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rheology&action=edit&section=3" title="Edit section: Dimensionless numbers"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Deborah_number">Deborah number</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rheology&action=edit&section=4" title="Edit section: Deborah number"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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/Deborah_number" title="Deborah number">Deborah number</a></div> <p>On one end of the spectrum we have an <a href="/wiki/Inviscid_flow" title="Inviscid flow">inviscid</a> or a simple Newtonian fluid and on the other end, a rigid solid; thus the behavior of all materials fall somewhere in between these two ends. The difference in material behavior is characterized by the level and nature of elasticity present in the material when it deforms, which takes the material behavior to the non-Newtonian regime. The non-dimensional Deborah number is designed to account for the degree of non-Newtonian behavior in a flow. The Deborah number is defined as the ratio of the characteristic time of relaxation (which purely depends on the material and other conditions like the temperature) to the characteristic time of experiment or observation.<sup id="cite_ref-deb1_3-1" class="reference"><a href="#cite_note-deb1-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><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> Small Deborah numbers represent Newtonian flow, while non-Newtonian (with both viscous and elastic effects present) behavior occurs for intermediate range Deborah numbers, and high Deborah numbers indicate an elastic/rigid solid. Since Deborah number is a relative quantity, the numerator or the denominator can alter the number. A very small Deborah number can be obtained for a fluid with extremely small relaxation time or a very large experimental time, for example. </p> <div class="mw-heading mw-heading3"><h3 id="Reynolds_number">Reynolds number</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rheology&action=edit&section=5" title="Edit section: Reynolds number"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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/Reynolds_number" title="Reynolds number">Reynolds number</a></div> <p>In <a href="/wiki/Fluid_mechanics" title="Fluid mechanics">fluid mechanics</a>, the <a href="/wiki/Reynolds_number" title="Reynolds number">Reynolds number</a> is a measure of the <a href="/wiki/Ratio" title="Ratio">ratio</a> of <a href="/wiki/Inertia" title="Inertia">inertial</a> <a href="/wiki/Force" title="Force">forces</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 v_{s}\rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{s}\rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b51ac5ec8628073095d32d5aa0491ae9d567473e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.333ex; height:2.176ex;" alt="{\displaystyle v_{s}\rho }"></span>) to <a href="/wiki/Viscosity" title="Viscosity">viscous</a> forces (<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 {\mu }{L}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>μ</mi> <mi>L</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\mu }{L}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8ba4ec93b0dc9a3e6c03b5cc2d9549c1f395238f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:2.419ex; height:4.843ex;" alt="{\displaystyle {\frac {\mu }{L}}}"></span>) and consequently it quantifies the relative importance of these two types of effect for given flow conditions. Under low Reynolds numbers viscous effects dominate and the flow is <a href="/wiki/Laminar_flow" title="Laminar flow">laminar</a>, whereas at high Reynolds numbers inertia predominates and the flow may be <a href="/wiki/Turbulent" class="mw-redirect" title="Turbulent">turbulent</a>. However, since rheology is concerned with fluids which do not have a fixed <a href="/wiki/Viscosity" title="Viscosity">viscosity</a>, but one which can vary with flow and time, calculation of the Reynolds number can be complicated. </p><p>It is one of the most important <a href="/wiki/Dimensionless_number" class="mw-redirect" title="Dimensionless number">dimensionless numbers</a> in <a href="/wiki/Fluid_dynamics" title="Fluid dynamics">fluid dynamics</a> and is used, usually along with other dimensionless numbers, to provide a criterion for determining <a href="/wiki/Dynamic_similitude" class="mw-redirect" title="Dynamic similitude">dynamic similitude</a>. When two geometrically similar flow patterns, in perhaps different fluids with possibly different flow rates, have the same values for the relevant dimensionless numbers, they are said to be dynamically similar. </p><p>Typically it is given as follows: </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 \mathrm {Re} ={\frac {\rho {\frac {u_{s}^{2}}{L}}}{\mu {\frac {u_{s}}{L^{2}}}}}={\frac {\rho u_{s}L}{\mu }}={\frac {u_{s}L}{\nu }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">e</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mi>L</mi> </mfrac> </mrow> </mrow> <mrow> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>ρ</mi> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mi>L</mi> </mrow> <mi>μ</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mi>L</mi> </mrow> <mi>ν</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {Re} ={\frac {\rho {\frac {u_{s}^{2}}{L}}}{\mu {\frac {u_{s}}{L^{2}}}}}={\frac {\rho u_{s}L}{\mu }}={\frac {u_{s}L}{\nu }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f716187946c867ac4e9b6471a9e0c3f46ead3bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.671ex; width:27.769ex; height:9.009ex;" alt="{\displaystyle \mathrm {Re} ={\frac {\rho {\frac {u_{s}^{2}}{L}}}{\mu {\frac {u_{s}}{L^{2}}}}}={\frac {\rho u_{s}L}{\mu }}={\frac {u_{s}L}{\nu }}}"></span></dd></dl> <p>where: </p> <ul><li><i>u</i><sub>s</sub> – mean <a href="/wiki/Flow_velocity" title="Flow velocity">flow velocity</a>, [m s<sup>−1</sup>]</li> <li><i>L</i> – characteristic length, [m]</li> <li><i>μ</i> – (absolute) dynamic <a href="/wiki/Fluid" title="Fluid">fluid</a> viscosity, [N s m<sup>−2</sup>] or [Pa s]</li> <li><i>ν</i> – kinematic fluid viscosity: <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 v={\frac {\mu }{\rho }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>μ</mi> <mi>ρ</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v={\frac {\mu }{\rho }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2322bd872ae5dc8fedf074eeb1dc336db29eb1a8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:6.464ex; height:5.343ex;" alt="{\displaystyle v={\frac {\mu }{\rho }}}"></span>, [m<sup>2</sup> s<sup>−1</sup>]</li> <li><i>ρ</i> – fluid <a href="/wiki/Density" title="Density">density</a>, [kg m<sup>−3</sup>].</li></ul> <div class="mw-heading mw-heading2"><h2 id="Measurement">Measurement</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rheology&action=edit&section=6" title="Edit section: Measurement"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Rheometer" title="Rheometer">Rheometers</a> are instruments used to characterize the rheological properties of materials, typically fluids that are melts or solution. These instruments impose a specific stress field or deformation to the fluid, and monitor the resultant deformation or stress. Instruments can be run in steady flow or oscillatory flow, in both shear and extension. </p> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rheology&action=edit&section=7" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Rheology has applications in <a href="/wiki/Materials_science" title="Materials science">materials science</a>, <a href="/wiki/Engineering" title="Engineering">engineering</a>, <a href="/wiki/Geophysics" title="Geophysics">geophysics</a>, <a href="/wiki/Physiology" title="Physiology">physiology</a>, human <a href="/wiki/Biology" title="Biology">biology</a> and <a href="/wiki/Pharmaceutics" title="Pharmaceutics">pharmaceutics</a>. Materials science is utilized in the production of many industrially important substances, such as <a href="/wiki/Cement" title="Cement">cement</a>, <a href="/wiki/Paint" title="Paint">paint</a>, and <a href="/wiki/Chocolate" title="Chocolate">chocolate</a>, which have complex flow characteristics. In addition, <a href="/wiki/Plasticity_(physics)" title="Plasticity (physics)">plasticity</a> theory has been similarly important for the design of metal forming processes. The science of rheology and the characterization of viscoelastic properties in the production and use of <a href="/wiki/Polymer" title="Polymer">polymeric</a> materials has been critical for the production of many products for use in both the industrial and military sectors. Study of flow properties of liquids is important for pharmacists working in the manufacture of several dosage forms, such as simple liquids, ointments, creams, pastes etc. The flow behavior of liquids under applied stress is of great relevance in the field of pharmacy. Flow properties are used as important quality control tools to maintain the superiority of the product and reduce batch to batch variations. </p> <div class="mw-heading mw-heading3"><h3 id="Materials_science">Materials science</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rheology&action=edit&section=8" title="Edit section: Materials science"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Polymers">Polymers</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rheology&action=edit&section=9" title="Edit section: Polymers"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Examples may be given to illustrate the potential applications of these principles to practical problems in the processing<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> and use of <a href="/wiki/Rubber" class="mw-redirect" title="Rubber">rubbers</a>, <a href="/wiki/Plastics" class="mw-redirect" title="Plastics">plastics</a>, and <a href="/wiki/Fiber" title="Fiber">fibers</a>. <a href="/wiki/Polymers" class="mw-redirect" title="Polymers">Polymers</a> constitute the basic materials of the rubber and plastic industries and are of vital importance to the textile, <a href="/wiki/Petroleum_industry" title="Petroleum industry">petroleum</a>, <a href="/wiki/Automobile_industry" class="mw-redirect" title="Automobile industry">automobile</a>, <a href="/wiki/Paper_industry" class="mw-redirect" title="Paper industry">paper</a>, and <a href="/wiki/Pharmaceutical_industries" class="mw-redirect" title="Pharmaceutical industries">pharmaceutical industries</a>. Their viscoelastic properties determine the mechanical performance of the final products of these industries, and also the success of processing methods at intermediate stages of production. </p><p>In <a href="/wiki/Viscoelasticity" title="Viscoelasticity">viscoelastic</a> materials, such as most polymers and plastics, the presence of liquid-like behaviour depends on the properties of and so varies with rate of applied load, i.e., how quickly a force is applied. The <a href="/wiki/Silicone" title="Silicone">silicone</a> toy '<a href="/wiki/Silly_Putty" title="Silly Putty">Silly Putty</a>' behaves quite differently depending on the time rate of applying a force. Pull on it slowly and it exhibits continuous flow, similar to that evidenced in a highly viscous liquid. Alternatively, when hit hard and directly, it shatters like a <a href="/wiki/Silicate_glass" class="mw-redirect" title="Silicate glass">silicate glass</a>. </p><p>In addition, conventional rubber undergoes a <a href="/wiki/Glass_transition" title="Glass transition">glass transition</a> (often called a <i>rubber-glass transition</i>). E.g. The <a href="/wiki/Space_Shuttle_Challenger" title="Space Shuttle Challenger">Space Shuttle <i>Challenger</i></a> disaster was caused by rubber O-rings that were being used well below their glass transition temperature on an unusually cold Florida morning, and thus could not flex adequately to form proper seals between sections of the two <a href="/wiki/Space_Shuttle_Solid_Rocket_Booster" title="Space Shuttle Solid Rocket Booster">solid-fuel rocket boosters</a>. </p> <div class="mw-heading mw-heading4"><h4 id="Biopolymers">Biopolymers</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rheology&action=edit&section=10" title="Edit section: Biopolymers"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Cellulose_strand.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Cellulose_strand.svg/300px-Cellulose_strand.svg.png" decoding="async" width="300" height="272" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Cellulose_strand.svg/450px-Cellulose_strand.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Cellulose_strand.svg/600px-Cellulose_strand.svg.png 2x" data-file-width="402" data-file-height="364" /></a><figcaption>Linear structure of <a href="/wiki/Cellulose" title="Cellulose">cellulose</a> — the most common component of all <a href="/wiki/Organic_matter" title="Organic matter">organic</a> plant life on Earth. * Note the evidence of <a href="/wiki/Hydrogen_bonding" class="mw-redirect" title="Hydrogen bonding">hydrogen bonding</a> which increases the <a href="/wiki/Viscosity" title="Viscosity">viscosity</a> at any temperature and pressure. This is an effect similar to that of <a href="/wiki/Polymer" title="Polymer">polymer</a> <a href="/wiki/Cross-link" title="Cross-link">crosslinking</a>, but less pronounced.</figcaption></figure> <div class="mw-heading mw-heading4"><h4 id="Sol-gel">Sol-gel</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rheology&action=edit&section=11" title="Edit section: Sol-gel"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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/Sol-gel" class="mw-redirect" title="Sol-gel">sol-gel</a></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Sol-gel_silicate_bonds.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/Sol-gel_silicate_bonds.svg/300px-Sol-gel_silicate_bonds.svg.png" decoding="async" width="300" height="410" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/Sol-gel_silicate_bonds.svg/450px-Sol-gel_silicate_bonds.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/10/Sol-gel_silicate_bonds.svg/600px-Sol-gel_silicate_bonds.svg.png 2x" data-file-width="220" data-file-height="301" /></a><figcaption><a href="/wiki/Polymerization" title="Polymerization">Polymerization</a> process of <a href="/wiki/Tetraethylorthosilicate" class="mw-redirect" title="Tetraethylorthosilicate">tetraethylorthosilicate</a> (TEOS) and water to form <a href="/wiki/Amorphous" class="mw-redirect" title="Amorphous">amorphous</a> <a href="/wiki/Hydrated" class="mw-redirect" title="Hydrated">hydrated</a> <a href="/wiki/Silica" class="mw-redirect" title="Silica">silica</a> particles (Si-OH) can be monitored <a href="/w/index.php?title=Rheolog&action=edit&redlink=1" class="new" title="Rheolog (page does not exist)">rheologically</a> by a number of different methods.</figcaption></figure> <p>With the <a href="/wiki/Viscosity" title="Viscosity">viscosity</a> of a <a href="/wiki/Sol_(colloid)" title="Sol (colloid)">sol</a> adjusted into a proper range, both <a href="/wiki/Optical" class="mw-redirect" title="Optical">optical</a> quality glass fiber and <a href="/wiki/Refractory" title="Refractory">refractory</a> ceramic fiber can be drawn which are used for <a href="/wiki/Fiber-optic_sensor" title="Fiber-optic sensor">fiber-optic sensors</a> and <a href="/wiki/Thermal_insulation" title="Thermal insulation">thermal insulation</a>, respectively. The mechanisms of <a href="/wiki/Hydrolysis" title="Hydrolysis">hydrolysis</a> and <a href="/wiki/Condensation" title="Condensation">condensation</a>, and the rheological factors that bias the structure toward linear or branched structures are the most critical issues of <a href="/wiki/Sol-gel" class="mw-redirect" title="Sol-gel">sol-gel</a> science and technology. </p> <div class="mw-heading mw-heading3"><h3 id="Geophysics">Geophysics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rheology&action=edit&section=12" title="Edit section: Geophysics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The scientific discipline of <a href="/wiki/Geophysics" title="Geophysics">geophysics</a> includes study of the flow of molten <a href="/wiki/Lava" title="Lava">lava</a> and study of debris flows (fluid mudslides). This disciplinary branch also deals with solid Earth materials which only exhibit flow over extended time-scales. Those that display viscous behaviour are known as <a href="/wiki/Rheid" title="Rheid">rheids</a>. For example, <a href="/wiki/Granite" title="Granite">granite</a> can flow plastically with a negligible yield stress at room temperatures (i.e. a viscous flow). Long-term creep experiments (~10 years) indicate that the viscosity of granite and glass under ambient conditions are on the order of 10<sup>20</sup> poises.<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><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> </p> <div class="mw-heading mw-heading3"><h3 id="Physiology">Physiology</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rheology&action=edit&section=13" title="Edit section: Physiology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Physiology includes the study of many bodily fluids that have complex structure and composition, and thus exhibit a wide range of viscoelastic flow characteristics. In particular there is a specialist study of blood flow called <a href="/wiki/Hemorheology" title="Hemorheology">hemorheology</a>. This is the study of flow properties of blood and its elements (<a href="/wiki/Blood_plasma" title="Blood plasma">plasma</a> and formed elements, including <a href="/wiki/Red_blood_cell" title="Red blood cell">red blood cells</a>, <a href="/wiki/White_blood_cell" title="White blood cell">white blood cells</a> and <a href="/wiki/Platelet" title="Platelet">platelets</a>). <a href="/wiki/Blood_viscosity" class="mw-redirect" title="Blood viscosity">Blood viscosity</a> is determined by plasma viscosity, <a href="/wiki/Hematocrit" title="Hematocrit">hematocrit</a> (volume fraction of red blood cell, which constitute 99.9% of the cellular elements) and mechanical behaviour of red blood cells. Therefore, red blood cell mechanics is the major determinant of flow properties of blood.(The ocular <a href="/wiki/Vitreous_humor" class="mw-redirect" title="Vitreous humor">Vitreous humor</a> is subject to rheologic observations, particularly during studies of age-related vitreous liquefaction, or <a href="/wiki/Synaeresis" title="Synaeresis">synaeresis</a>.)<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><p>The leading characteristic for hemorheology has been <a href="/wiki/Shear_thinning" title="Shear thinning">shear thinning</a> in steady shear flow. Other non-Newtonian rheological characteristics that blood can demonstrate includes <a href="/wiki/Pseudoplasticity" class="mw-redirect" title="Pseudoplasticity">pseudoplasticity</a>, <a href="/wiki/Viscoelasticity" title="Viscoelasticity">viscoelasticity</a>, and <a href="/wiki/Thixotropy" title="Thixotropy">thixotropy</a>.<sup id="cite_ref-Beris-2021_15-0" class="reference"><a href="#cite_note-Beris-2021-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Red_blood_cell_aggregation">Red blood cell aggregation</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rheology&action=edit&section=14" title="Edit section: Red blood cell aggregation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>There are two current major hypotheses to explain blood flow predictions and <a href="/wiki/Shear_thinning" title="Shear thinning">shear thinning</a> responses. The two models also attempt to demonstrate the drive for reversible red blood cell aggregation, although the mechanism is still being debated. There is a direct effect of red blood cell aggregation on blood viscosity and circulation.<sup id="cite_ref-Lee-2017_16-0" class="reference"><a href="#cite_note-Lee-2017-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> The foundation of <a href="/wiki/Hemorheology" title="Hemorheology">hemorheology</a> can also provide information for modeling of other biofluids.<sup id="cite_ref-Beris-2021_15-1" class="reference"><a href="#cite_note-Beris-2021-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> The bridging or "cross-bridging" hypothesis suggests that macromolecules physically crosslink adjacent red blood cells into rouleaux structures. This occurs through adsorption of macromolecules onto the red blood cell surfaces.<sup id="cite_ref-Beris-2021_15-2" class="reference"><a href="#cite_note-Beris-2021-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Lee-2017_16-1" class="reference"><a href="#cite_note-Lee-2017-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> The depletion layer hypothesis suggests the opposite mechanism. The surfaces of the red blood cells are bound together by an osmotic pressure gradient that is created by depletion layers overlapping.<sup id="cite_ref-Beris-2021_15-3" class="reference"><a href="#cite_note-Beris-2021-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> The effect of rouleaux aggregation tendency can be explained by <a href="/wiki/Hematocrit" title="Hematocrit">hematocrit</a> and fibrinogen concentration in whole blood rheology.<sup id="cite_ref-Beris-2021_15-4" class="reference"><a href="#cite_note-Beris-2021-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> Some techniques researchers use are optical trapping and microfluidics to measure cell interaction in vitro.<sup id="cite_ref-Lee-2017_16-2" class="reference"><a href="#cite_note-Lee-2017-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Disease_and_diagnostics">Disease and diagnostics</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rheology&action=edit&section=15" title="Edit section: Disease and diagnostics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Changes to viscosity has been shown to be linked with diseases like hyperviscosity, hypertension, sickle cell anemia, and diabetes.<sup id="cite_ref-Beris-2021_15-5" class="reference"><a href="#cite_note-Beris-2021-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Hemorheological" class="mw-redirect" title="Hemorheological">Hemorheological</a> measurements and genomic testing technologies act as preventative measures and diagnostic tools.<sup id="cite_ref-Beris-2021_15-6" class="reference"><a href="#cite_note-Beris-2021-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Hemorheology" title="Hemorheology">Hemorheology</a> has also been correlated with aging effects, especially with impaired blood fluidity, and studies have shown that physical activity may improve the thickening of blood rheology.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Zoology">Zoology</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rheology&action=edit&section=16" title="Edit section: Zoology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Many animals make use of rheological phenomena, for example <a href="/wiki/Scincus_scincus" title="Scincus scincus">sandfish</a> that exploit the granular rheology of dry sand to "swim" in it or <a href="/wiki/Gastropoda" title="Gastropoda">land gastropods</a> that use <a href="/wiki/Snail_slime" title="Snail slime">snail slime</a> for adhesive <a href="/wiki/Animal_locomotion" title="Animal locomotion">locomotion</a>. Certain animals produce specialized <a href="/wiki/Endogeny" class="mw-redirect" title="Endogeny">endogenous</a> <a href="/wiki/Complex_fluid" title="Complex fluid">complex fluids</a>, such as the sticky slime produced by <a href="/wiki/Velvet_worm" class="mw-redirect" title="Velvet worm">velvet worms</a> to immobilize prey or the fast-gelling underwater slime secreted by <a href="/wiki/Hagfish" title="Hagfish">hagfish</a> to deter predators.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Food_rheology">Food rheology</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rheology&action=edit&section=17" title="Edit section: Food rheology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Food_rheology" title="Food rheology">Food rheology</a> is important in the manufacture and processing of food products, such as cheese<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> and <a href="/wiki/Gelato" title="Gelato">gelato</a>.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> An adequate rheology is important for the indulgence of many common foods, particularly in the case of sauces,<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> dressings,<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> <a href="/wiki/Yogurt" title="Yogurt">yogurt</a>,<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> or <a href="/wiki/Fondue" title="Fondue">fondue</a>.<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> </p><p><a href="/wiki/Thickening_agents" class="mw-redirect" title="Thickening agents">Thickening agents</a>, or thickeners, are substances which, when added to an aqueous mixture, increase its <a href="/wiki/Viscosity" title="Viscosity">viscosity</a> without substantially modifying its other properties, such as taste. They provide body, increase <a href="/wiki/Strength_of_materials" title="Strength of materials">stability</a>, and improve <a href="/wiki/Suspension_(chemistry)" title="Suspension (chemistry)">suspension</a> of added ingredients. Thickening agents are often used as <a href="/wiki/Food_additive" title="Food additive">food additives</a> and in <a href="/wiki/Cosmetics" title="Cosmetics">cosmetics</a> and <a href="/wiki/Personal_hygiene_product" class="mw-redirect" title="Personal hygiene product">personal hygiene products</a>. Some thickening agents are <b>gelling agents</b>, forming a <a href="/wiki/Gel" title="Gel">gel</a>. The agents are materials used to thicken and stabilize liquid solutions, <a href="/wiki/Emulsion" title="Emulsion">emulsions</a>, and <a href="/wiki/Suspension_(chemistry)" title="Suspension (chemistry)">suspensions</a>. They dissolve in the liquid phase as a <a href="/wiki/Colloid" title="Colloid">colloid</a> mixture that forms a weakly cohesive internal structure. Food thickeners frequently are based on either <a href="/wiki/Polysaccharide" title="Polysaccharide">polysaccharides</a> (<a href="/wiki/Starch" title="Starch">starches</a>, <a href="/wiki/Vegetable_gum" class="mw-redirect" title="Vegetable gum">vegetable gums</a>, and <a href="/wiki/Pectin" title="Pectin">pectin</a>), or <a href="/wiki/Protein" title="Protein">proteins</a>.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup><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> <div class="mw-heading mw-heading3"><h3 id="Concrete_rheology">Concrete rheology</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rheology&action=edit&section=18" title="Edit section: Concrete rheology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Concrete" title="Concrete">Concrete</a>'s and <a href="/wiki/Mortar_(masonry)" title="Mortar (masonry)">mortar</a>'s workability is related to the rheological properties of the fresh <a href="/wiki/Cement" title="Cement">cement</a> paste. The mechanical properties of hardened concrete increase if less water is used in the concrete mix design, however reducing the water-to-cement ratio may decrease the ease of mixing and application. To avoid these undesired effects, <a href="/wiki/Superplasticizer" title="Superplasticizer">superplasticizers</a> are typically added to decrease the apparent yield stress and the viscosity of the fresh paste. Their addition highly improves concrete and mortar properties.<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="Filled_polymer_rheology">Filled polymer rheology</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rheology&action=edit&section=19" title="Edit section: Filled polymer rheology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The incorporation of various types of <a href="/wiki/Filler_(materials)" title="Filler (materials)">fillers</a> into <a href="/wiki/Polymer" title="Polymer">polymers</a> is a common means of reducing cost and to impart certain desirable mechanical, thermal, electrical and magnetic properties to the resulting material. The advantages that filled polymer systems have to offer come with an increased complexity in the rheological behavior.<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><p>Usually when the use of fillers is considered, a compromise has to be made between the improved mechanical properties in the solid state on one side and the increased difficulty in melt processing, the problem of achieving uniform <a href="/wiki/Dispersion_(chemistry)" title="Dispersion (chemistry)">dispersion</a> of the filler in the polymer matrix and the economics of the process due to the added step of compounding on the other. The rheological properties of filled polymers are determined not only by the type and amount of filler, but also by the shape, size and size distribution of its particles. The viscosity of filled systems generally increases with increasing filler fraction. This can be partially ameliorated via broad particle size distributions via the <a href="/wiki/Farris_effect_(rheology)" title="Farris effect (rheology)">Farris effect</a>. An additional factor is the <a href="/wiki/Stress_(mechanics)" title="Stress (mechanics)">stress</a> transfer at the filler-polymer interface. The interfacial adhesion can be substantially enhanced via a coupling agent that adheres well to both the polymer and the filler particles. The type and amount of <a href="/wiki/Surface_treatment" class="mw-redirect" title="Surface treatment">surface treatment</a> on the filler are thus additional parameters affecting the rheological and material properties of filled polymeric systems. </p><p>It is important to take into consideration wall slip when performing the rheological characterization of highly filled materials, as there can be a large difference between the actual strain and the measured strain.<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-heading2"><h2 id="Rheologist">Rheologist</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rheology&action=edit&section=20" title="Edit section: Rheologist"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Unreferenced plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Rheology" title="Special:EditPage/Rheology">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>.<br /><small><span class="plainlinks"><i>Find sources:</i> <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&q=%22Rheology%22">"Rheology"</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22Rheology%22+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Rheology%22&tbs=bkt:s&tbm=bks">newspapers</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?tbs=bks:1&q=%22Rheology%22+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Rheology%22">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Rheology%22&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">May 2023</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>A rheologist is an <a href="/wiki/Interdisciplinary" class="mw-redirect" title="Interdisciplinary">interdisciplinary</a> scientist or engineer who studies the flow of complex liquids or the deformation of soft solids. It is not a primary degree subject; there is no qualification of rheologist as such. Most rheologists have a qualification in mathematics, the physical sciences (e.g. <a href="/wiki/Chemistry" title="Chemistry">chemistry</a>, <a href="/wiki/Physics" title="Physics">physics</a>, <a href="/wiki/Geology" title="Geology">geology</a>, <a href="/wiki/Biology" title="Biology">biology</a>), engineering (e.g. <a href="/wiki/Mechanical_engineering" title="Mechanical engineering">mechanical</a>, <a href="/wiki/Chemical_engineering" title="Chemical engineering">chemical</a>, <a href="/wiki/Materials_science" title="Materials science">materials science, plastics engineering and engineering</a> or <a href="/wiki/Civil_engineering" title="Civil engineering">civil engineering</a>), <a href="/wiki/Medicine" title="Medicine">medicine</a>, or certain technologies, notably <a href="/wiki/Materials_science" title="Materials science">materials</a> or <a href="/wiki/Food_science" title="Food science">food</a>. Typically, a small amount of rheology may be studied when obtaining a degree, but a person working in rheology will extend this knowledge during postgraduate research or by attending short courses and by joining a professional association. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rheology&action=edit&section=21" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Bingham_plastic" title="Bingham plastic">Bingham plastic</a></li> <li><a href="/wiki/Die_swell" title="Die swell">Die swell</a></li> <li><a href="/wiki/Fluid_dynamics" title="Fluid dynamics">Fluid dynamics</a></li> <li><a href="/wiki/Glass_transition" title="Glass transition">Glass transition</a></li> <li><a href="/wiki/Interfacial_rheology" title="Interfacial rheology">Interfacial rheology</a></li> <li><a href="/wiki/Liquid" title="Liquid">Liquid</a></li> <li><a href="/wiki/List_of_rheologists" title="List of rheologists">List of rheologists</a></li> <li><a href="/wiki/Microrheology" title="Microrheology">Microrheology</a></li> <li><a href="/wiki/Nordic_Rheology_Society" title="Nordic Rheology Society">Nordic Rheology Society</a><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></li> <li><a href="/wiki/Rheological_weldability" title="Rheological weldability">Rheological weldability</a> for thermoplastics</li> <li><a href="/wiki/Rheopectic" class="mw-redirect" title="Rheopectic">Rheopectic</a></li> <li><a href="/wiki/Solid" title="Solid">Solid</a></li> <li><a href="/wiki/Transport_phenomena" title="Transport phenomena">Transport phenomena</a></li> <li><a href="/wiki/%CE%9C(I)_rheology" title="Μ(I) rheology">μ(I) rheology</a>: one model of the rheology of a granular flow.</li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rheology&action=edit&section=22" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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-Schowalter-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-Schowalter_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Schowalter_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Schowalter_1-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text">W. R. Schowalter (1978) Mechanics of Non-Newtonian Fluids Pergamon <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/0-08-021778-8" title="Special:BookSources/0-08-021778-8">0-08-021778-8</a></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJames_Freeman_Steffe1996" class="citation book cs1">James Freeman Steffe (1 January 1996). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=LrrdONuST9kC"><i>Rheological Methods in Food Process Engineering</i></a>. Freeman Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-9632036-1-8" title="Special:BookSources/978-0-9632036-1-8"><bdi>978-0-9632036-1-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Rheological+Methods+in+Food+Process+Engineering&rft.pub=Freeman+Press&rft.date=1996-01-01&rft.isbn=978-0-9632036-1-8&rft.au=James+Freeman+Steffe&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DLrrdONuST9kC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARheology" class="Z3988"></span></span> </li> <li id="cite_note-deb1-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-deb1_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-deb1_3-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://rrc.engr.wisc.edu/deborah.html">The Deborah Number</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110413144406/http://rrc.engr.wisc.edu/deborah.html">Archived</a> 2011-04-13 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></span> </li> <li id="cite_note-Barnes1982-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-Barnes1982_4-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBarnes1982" class="citation book cs1">Barnes, Jonathan (1982). <i>The presocratic philosophers</i>. Routledge. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-415-05079-1" title="Special:BookSources/978-0-415-05079-1"><bdi>978-0-415-05079-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+presocratic+philosophers&rft.pub=Routledge&rft.date=1982&rft.isbn=978-0-415-05079-1&rft.aulast=Barnes&rft.aufirst=Jonathan&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARheology" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBerisGiacomin2014" class="citation journal cs1">Beris, A. N.; Giacomin, A. J. (2014). "πάντα ῥεῖ : Everything Flows". <i>Applied Rheology</i>. <b>24</b>: 52918. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.3933%2FApplRheol-24-52918">10.3933/ApplRheol-24-52918</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:195789095">195789095</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Applied+Rheology&rft.atitle=%CF%80%CE%AC%CE%BD%CF%84%CE%B1+%E1%BF%A5%CE%B5%E1%BF%96+%3A+Everything+Flows&rft.volume=24&rft.pages=52918&rft.date=2014&rft_id=info%3Adoi%2F10.3933%2FApplRheol-24-52918&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A195789095%23id-name%3DS2CID&rft.aulast=Beris&rft.aufirst=A.+N.&rft.au=Giacomin%2C+A.+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARheology" class="Z3988"></span></span> </li> <li id="cite_note-bird1-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-bird1_6-0">^</a></b></span> <span class="reference-text">R. B. Bird, W. E. Stewart, E. N. Lightfoot (1960), Transport Phenomena, John Wiley & Sons, <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/0-471-07392-X" title="Special:BookSources/0-471-07392-X">0-471-07392-X</a>.<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (June 2024)">page needed</span></a></i>]</sup></span> </li> <li id="cite_note-bird2-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-bird2_7-0">^</a></b></span> <span class="reference-text">R. Byrin Bird, Charles F. Curtiss, Robert C. Armstrong (1989), Dynamics of Polymeric Liquids, Vol 1 & 2, Wiley Interscience, <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/0-471-51844-1" title="Special:BookSources/0-471-51844-1">0-471-51844-1</a> and 978-0471518440.<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (June 2024)">page needed</span></a></i>]</sup></span> </li> <li id="cite_note-morris1-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-morris1_8-0">^</a></b></span> <span class="reference-text">Faith A. Morrison (2001), Understanding Rheology, Oxford University Press, <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/0-19-514166-0" title="Special:BookSources/0-19-514166-0">0-19-514166-0</a> and 978-0195141665.<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (June 2024)">page needed</span></a></i>]</sup></span> </li> <li id="cite_note-creep1-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-creep1_9-0">^</a></b></span> <span class="reference-text">William N. Findley, James S. Lai, Kasif Onaran (1989), Creep and Relaxation of Nonlinear Viscoelastic Materials, Dover Publications</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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFReiner1964" class="citation journal cs1">Reiner, M. (1964). "The Deborah Number". <i>Physics Today</i>. <b>17</b> (1): 62. <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/1964PhT....17a..62R">1964PhT....17a..62R</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%2F1.3051374">10.1063/1.3051374</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Today&rft.atitle=The+Deborah+Number&rft.volume=17&rft.issue=1&rft.pages=62&rft.date=1964&rft_id=info%3Adoi%2F10.1063%2F1.3051374&rft_id=info%3Abibcode%2F1964PhT....17a..62R&rft.aulast=Reiner&rft.aufirst=M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARheology" class="Z3988"></span></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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShenoySaini1996" class="citation book cs1">Shenoy, Aroon V.; Saini, D. 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Retrieved <span class="nowrap">2021-12-01</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=uia.org&rft.atitle=Nordic+Rheology+Society+%7C+UIA+Yearbook+Profile+%7C+Union+of+International+Associations&rft_id=https%3A%2F%2Fuia.org%2Fs%2For%2Fen%2F1100064780&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARheology" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Rheology&action=edit&section=23" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid 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href="https://en.wiktionary.org/wiki/Special:Search/rheology" class="extiw" title="wiktionary:Special:Search/rheology">rheology</a></b></i> in Wiktionary, the free dictionary.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="http://www.rheology.org/sor/publications/rheology_b/jan02/origin_of_rheology.pdf">"The Origins of Rheology: A short historical excursion"</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190819032440/http://www.rheology.org/sor/publications/rheology_b/jan02/origin_of_rheology.pdf">Archived</a> 2019-08-19 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> by Deepak Doraiswamy, DuPont iTechnologies</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20160316132753/http://www.rheotest.de/english/company/history">RHEOTEST Medingen GmbH</a> – Short history and collection of rheological instruments from the time of Fritz Höppler</li> <li><a rel="nofollow" class="external autonumber" href="http://www.rheology.org/sor/publications/rheology_b/RB2014Jul.pdf">[2]</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20181220171954/http://www.rheology.org/sor/publications/rheology_b/RB2014Jul.pdf">Archived</a> 2018-12-20 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> - On the Rheology of Cats</li></ul> <dl><dt>Societies</dt></dl> <ul><li><a rel="nofollow" class="external text" href="http://www.rheology.org/sor/">American Society of Rheology</a></li> <li><a rel="nofollow" class="external text" href="http://www.rheology.org.au/">Australian Society of Rheology</a></li> <li><a rel="nofollow" class="external text" href="http://www.bsr.org.uk/">British Society of Rheology</a></li> <li><a rel="nofollow" class="external text" href="http://www.rheology-esr.net/">European Society of Rheology</a></li> <li><a rel="nofollow" class="external text" href="http://www.legfr.fr/">French Society of Rheology</a></li> <li><a rel="nofollow" class="external text" href="https://nordicrheologysociety.org/">Nordic Rheology Society</a></li> <li><a rel="nofollow" class="external text" href="http://reologie.ro/">Romanian Society of Rheology</a></li> <li><a rel="nofollow" class="external text" href="https://www.rheology.or.kr/">Korean Society of Rheology</a></li></ul> <dl><dt>Journals</dt></dl> <ul><li><i><a rel="nofollow" class="external text" href="http://www.ar.ethz.ch/">Applied Rheology</a></i></li> <li><i><a rel="nofollow" class="external text" href="http://www.journals.elsevier.com/journal-of-non-newtonian-fluid-mechanics/">Journal of Non-Newtonian Fluid Mechanics</a></i></li> <li><i><a rel="nofollow" class="external text" href="http://www.journalofrheology.org/">Journal of Rheology</a></i></li> <li><i><a rel="nofollow" class="external text" href="https://link.springer.com/journal/397">Rheologica Acta</a></i></li></ul> <div class="navbox-styles"><link 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