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A., Stability of Non-linear Constitutive Formulations for Viscoelastic Fluids, Springer, New York, 2014] in this series is an attempt to give an overall comprehensive view of a" /> <title>(PDF) Developments in the Flow of Complex Fluids in Tubes</title> <link rel="canonical" href="https://www.academia.edu/44275018/Developments_in_the_Flow_of_Complex_Fluids_in_Tubes" /> <script async src="https://www.googletagmanager.com/gtag/js?id=G-5VKX33P2DS"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-5VKX33P2DS', { cookie_domain: 'academia.edu', send_page_view: false, }); gtag('event', 'page_view', { 'controller': "single_work", 'action': "show", 'controller_action': 'single_work#show', 'logged_in': 'false', 'edge': 'unknown', // Send nil if there is no A/B test bucket, in case some records get logged // with missing data - that way we can distinguish between the two cases. // ab_test_bucket should be of the form <ab_test_name>:<bucket> 'ab_test_bucket': null, }) </script> <script> var $controller_name = 'single_work'; var $action_name = "show"; var $rails_env = 'production'; var $app_rev = '3396cc84cfd2f38327776bf96002dae06ee5bf2b'; var $domain = 'academia.edu'; var $app_host = "academia.edu"; var $asset_host = "academia-assets.com"; var $start_time = new Date().getTime(); var $recaptcha_key = "6LdxlRMTAAAAADnu_zyLhLg0YF9uACwz78shpjJB"; var $recaptcha_invisible_key = "6Lf3KHUUAAAAACggoMpmGJdQDtiyrjVlvGJ6BbAj"; var $disableClientRecordHit = false; </script> <script> window.require = { config: function() { return function() {} } } </script> <script> window.Aedu = window.Aedu || {}; window.Aedu.hit_data = null; window.Aedu.serverRenderTime = new Date(1736257382000); window.Aedu.timeDifference = new Date().getTime() - 1736257382000; </script> <script type="application/ld+json">{"@context":"https://schema.org","@type":"ScholarlyArticle","abstract":"This monograph together with its complimentary volume [Siginer, D. A., Stability of Non-linear Constitutive Formulations for Viscoelastic Fluids, Springer, New York, 2014] in this series is an attempt to give an overall comprehensive view of a complex field, only 60 or so years old, still far from being settled on firm grounds, that of the dynamics of viscoelastic fluid flow and suspension flow in tubes. The monograph on “Stability of Non-linear Constitutive Formulations for Viscoelastic Fluid Media” covers the development of constitutive equation formulations for viscoelastic fluids in their historical context together with the latest progress made, and this volume covers the state-of-the-art knowledge in predicting the flow of viscoelastic fluids and suspensions in tubes highlighting the historical as well as the most recent findings. Most if not all viscoelastic fluids in industrial manufacturing processes flow in laminar regime through tubes, which are not necessarily circular, at one time or another during the processing of the material. Laminar regime is by far the predominant flow mode for viscoelastic fluids encountered in manufacturing processes, and it is extensively covered in this monograph. Turbulent flow of dilute viscoelastic solutions is a topic which has not received much attention except when related to drag reduction. For particle-laden flows there are very interesting developments in both laminar and turbulent regime, and they are duly covered. It is critically important that the flow of non-linear viscoelastic fluids and suspensions in tubes can be predicted on a sound basis, thus the raison d’eˆtre of this volume. As flow behavior predictions are directly related to the constitutive formulations used, this volume relies heavily on the volume on [Siginer, D. A., Stability of Non-linear Constitutive Formulations for Viscoelastic Fluids, Springer, New York, 2014]. The science of rheology defined as the study of the deformation and flow of matter was virtually single-handedly founded and the name invented by Professor Bingham of Lafayette College in the late 1920s. Rheology is a wide encompassing science which covers the study of the deformation and flow of diverse materials such as polymers, suspensions, asphalt, lubricants, paints, plastics, rubber, and biofluids, all of which display non-Newtonian behavior when subjected to external stimuli and as a result deform and flow in a manner not predictable by Newtonian mechanics. The development of rheology, which had gotten to a slow start, took a boost during WWII as materials used in various applications, in flame throwers, for instance, were found to be viscoelastic. As Truesdell and Noll famously wrote [Truesdell, C. and Noll, W., the Non-Linear Field Theories of Mechanics, 2nd ed., Springer, Berlin, 1992] “By 1949 all work on the foundations of Rheology done before 1945 had been rendered obsolete.” In the years following WWII, the emergence and rapid growth of the synthetic fiber and polymer processing industries, appearance of liquid detergents, multigrade oils, non-drip paints, and contact adhesives, and developments in pharmaceutical and food industries and biotechnology spurred the development of rheology. All these examples clearly illustrate the relevance of rheological studies to life and industry. The reliance of all these fields on rheological studies is at the very basis of many if not all of the amazing developments and success stories ending up with many of the products used by the public at large in everyday life. Non-Newtonian fluid mechanics, which is an integral part of rheology, really made big strides only after WWII and has been developing at a rapid rate ever since. The development of reliable constitutive formulations to predict the behavior of flowing substances with non-linear stress–strain relationships is quite a difficult proposition by comparison with Newtonian fluid mechanics with linear stress–strain relationship. The latter does enjoy a head start of two centuries tracing back its inception to Newton and luminaries like Euler and Bernoulli. With the former the non-linear structure does not allow the merging of the constitutive equations for the stress components with the linear momentum equation as it is the case with Newtonian fluids ending up with the Navier–Stokes equations. Thus, the practitioner ends up with six additional scalar equations to be solved in three dimensions for the six independent components of the symmetric stress tensor. The difficulties in solving in tandem this set of non-linear field equations, which may involve both inertial and constitutive non-linearities, cannot be underestimated. Perhaps equally importantly at this point in time in the unfolding development of the science, we are not fortunate enough to have developed a single constitutive formulation for viscoelastic fluids, which may lend itself to most applications and yield reasonably accurate predictions together with the…","author":[{"@context":"https://schema.org","@type":"Person","name":"Dennis A . Siginer"}],"contributor":[],"dateCreated":"2020-10-11","dateModified":"2020-10-11","datePublished":"2015-01-01","headline":"Developments in the Flow of Complex Fluids in Tubes","identifier":{"@type":"PropertyValue","propertyID":"DOI","value":"10.1007/978-3-319-02426-4"},"image":"https://attachments.academia-assets.com/64652860/thumbnails/1.jpg","inLanguage":"en","keywords":["Engineering Physics","Applied Mathematics","Mass Transfer","Fluid Mechanics","Multiphase Flow","Continuum Mechanics","Fluid Dynamics","Engineering Mathematics","Heat and Mass Transfer","Multiphase flows","Applied mathematics and Modelling","Non-newtonian Fluid Mechanics","Particle-laden Flow"],"publication":"Developments in the Flow of Complex Fluids in 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{"work":{"id":44275018,"created_at":"2020-10-11T13:08:17.979-07:00","from_world_paper_id":null,"updated_at":"2023-06-13T11:03:59.275-07:00","_data":{"doi":"10.1007/978-3-319-02426-4","abstract":"This monograph together with its complimentary volume [Siginer, D. A., Stability of Non-linear Constitutive Formulations for Viscoelastic Fluids, Springer, New York, 2014] in this series is an attempt to give an overall comprehensive view of a complex field, only 60 or so years old, still far from being settled on firm grounds, that of the dynamics of viscoelastic fluid flow and suspension flow in tubes. The monograph on “Stability of Non-linear Constitutive Formulations for Viscoelastic Fluid Media” covers the development of constitutive equation formulations for viscoelastic fluids in their historical context together with the latest progress made, and this volume covers the state-of-the-art knowledge in predicting the flow of viscoelastic fluids and suspensions in tubes highlighting the historical as well as the most recent findings. Most if not all viscoelastic fluids in industrial manufacturing processes flow in laminar regime through tubes, which are not necessarily circular, at one time or another during the processing of the material. Laminar regime is by far the predominant flow mode for viscoelastic fluids encountered in manufacturing processes, and it is extensively covered in this monograph. Turbulent flow of dilute viscoelastic solutions is a topic which has not received much attention except when related to drag reduction. For particle-laden flows there are very interesting developments in both laminar and turbulent regime, and they are duly covered. It is critically important that the flow of non-linear viscoelastic fluids and suspensions in tubes can be predicted on a sound basis, thus the raison d’eˆtre of this volume. As flow behavior predictions are directly related to the constitutive formulations used, this volume relies heavily on the volume on [Siginer, D. A., Stability of Non-linear Constitutive Formulations for Viscoelastic Fluids, Springer, New York, 2014]. \nThe science of rheology defined as the study of the deformation and flow of matter was virtually single-handedly founded and the name invented by Professor Bingham of Lafayette College in the late 1920s. Rheology is a wide encompassing science which covers the study of the deformation and flow of diverse materials such as polymers, suspensions, asphalt, lubricants, paints, plastics, rubber, and biofluids, all of which display non-Newtonian behavior when subjected to external stimuli and as a result deform and flow in a manner not predictable by Newtonian mechanics.\nThe development of rheology, which had gotten to a slow start, took a boost during WWII as materials used in various applications, in flame throwers, for instance, were found to be viscoelastic. As Truesdell and Noll famously wrote [Truesdell, C. and Noll, W., the Non-Linear Field Theories of Mechanics, 2nd ed., Springer, Berlin, 1992] “By 1949 all work on the foundations of Rheology done before 1945 had been rendered obsolete.” In the years following WWII, the emergence and rapid growth of the synthetic fiber and polymer processing industries, appearance of liquid detergents, multigrade oils, non-drip paints, and contact adhesives, and developments in pharmaceutical and food industries and biotechnology spurred the development of rheology. All these examples clearly illustrate the relevance of rheological studies to life and industry. The reliance of all these fields on rheological studies is at the very basis of many if not all of the amazing developments and success stories ending up with many of the products used by the public at large in everyday life.\nNon-Newtonian fluid mechanics, which is an integral part of rheology, really made big strides only after WWII and has been developing at a rapid rate ever since. The development of reliable constitutive formulations to predict the behavior of flowing substances with non-linear stress–strain relationships is quite a difficult proposition by comparison with Newtonian fluid mechanics with linear stress–strain relationship. The latter does enjoy a head start of two centuries tracing back its inception to Newton and luminaries like Euler and Bernoulli. With the former the non-linear structure does not allow the merging of the constitutive equations for the stress components with the linear momentum equation as it is the case with Newtonian fluids ending up with the Navier–Stokes equations. Thus, the practitioner ends up with six additional scalar equations to be solved in three dimensions for the six independent components of the symmetric stress tensor. The difficulties in solving in tandem this set of non-linear field equations, which may involve both inertial and constitutive non-linearities, cannot be underestimated. Perhaps equally importantly at this point in time in the unfolding development of the science, we are not fortunate enough to have developed a single constitutive formulation for viscoelastic fluids, which may lend itself to most applications and yield reasonably accurate predictions together with the field balance equations. The field is littered with a plethora of equations, some of which may yield reasonable predictions in some flows and utterly unacceptable predictions in others. Thus, we end up with classes of equations for viscoelastic fluids that would apply to classes of flows and fluids, an ad hoc concept at best that hopefully will give way one day to a universal equation, which may apply to all fluids in all motions. In addition the stability of these equations is a very important issue. Any given constitutive equation should be stable in the Hadamard and dissipative sense and should not violate the basic principles of thermodynamics.\nDynamics of tube flow of non-Brownian suspensions and its underpinning field turbulent motion of linear (Newtonian) fluids shows interesting similarities with the flow of viscoelastic fluids in that the secondary flows of viscoelastic fluids in laminar flow driven by unbalanced normal stresses have a counterpart in the turbulent motion of linear fluids in straight tubes of non-circular cross section and in the laminar motion of particle-laden linear fluids. The latter secondary flows are driven by normal stresses due to shear-induced migration of particles. This is a new topic of hot research thrust given its implications in applications. The direction of these normal stresses is opposite of those present in the flow field of a viscoelastic fluid. In fact the tying thread among these seemingly different motions is that all are driven by normal stresses. The turbulent flow of linear fluids is known to have a transversal field due to the anisotropy of the Reynolds stress tensor in non-circular cross sections which entails unbalanced normal Reynolds stresses in the cross section perpendicular to the axial direction. Secondary field also exists in the turbulent flow of linear fluids in circular cross sections if the symmetry is somehow broken due, for example, to unevenly distributed roughness on the boundary, which would again trigger anisotropy of the Reynolds stress tensor. It is not possible to develop a good understanding of the mechanics of the secondary field both in laminar and turbulent motion of particle-laden fluids without a clear grasp of the underlying mechanics of the turbulent secondary field of homogeneous linear fluids. Thus a complete review of both is presented including interesting constitutive similarities with viscoelastic fluids which do arise when certain non-linear closure approximations are made for the anisotropic part of the Reynolds stress tensor.\nThe impact of the secondary flows on engineering calculations is particularly important as turbulent flows in ducts of non-circular cross section are often encountered in engineering practice. Some examples are flows in heat exchangers, ventilation and air-conditioning systems, nuclear reactors, impellers, blade passages, aircraft intakes, and turbomachinery. If neglected significant errors may be introduced\nin the design as secondary flows lead to additional friction losses and can shift the location of the maximum momentum transport from the duct centerline. The secondary velocity depends on cross-sectional coordinates alone and therefore is independent of end effects. It is only of the order of 1–3 % of the streamwise bulk velocity, but by transporting high-momentum fluid toward the corners, it distorts substantially the cross-sectional equal axial velocity lines; specifically it causes a bulging of the velocity contours toward the corners with important consequences\nsuch as considerable friction losses. The need for turbulence models that can reliably predict the secondary flows that may occur in engineering applications is of paramount importance.\nEfforts have not been spared to be thorough in the presentation with commentaries about the successes and failures of each theory and the reasons behind them. The link between..... \nPalapye, Botswana and Santiago, Chile \nDennis A. Siginer\n","publication_date":"2015,,","publication_name":"Developments in the Flow of Complex Fluids in Tubes"},"document_type":"book","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Developments in the Flow of Complex Fluids in Tubes","broadcastable":true,"draft":false,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [33969261]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "control"; window.loswp.useOptimizedScribd4genScript = false; window.loginModal = {}; window.loginModal.appleClientId = 'edu.academia.applesignon';</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{"location":"swp-splash-paper-cover","attachmentId":64652860,"attachmentType":"pdf"}"><img alt="First page of “Developments in the Flow of Complex Fluids in Tubes”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/64652860/mini_magick20201011-25372-1w2h97j.png?1602447054" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/images/single_work_splash/adobe_icon.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">Developments in the Flow of Complex Fluids in Tubes</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="33969261" href="https://usach.academia.edu/DennisSiginer"><img alt="Profile image of Dennis A . Siginer" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/33969261/11229757/12529882/s65_dennis.siginer.jpg" />Dennis A . Siginer</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">2015, Developments in the Flow of Complex Fluids in Tubes</p><a class="js-loswp-work-card-doi-link ds2-5-body-sm ds2-5-body-link" href="https://doi.org/10.1007/978-3-319-02426-4" rel="nofollow">https://doi.org/10.1007/978-3-319-02426-4</a><div class="ds-work-card--work-metadata"><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">visibility</span><p class="ds2-5-body-sm" id="work-metadata-view-count">…</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">description</span><p class="ds2-5-body-sm">1 page</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">link</span><p class="ds2-5-body-sm">2 files</p></div></div><script>(async () => { const workId = 44275018; const worksViewsPath = "/v0/works/views?subdomain_param=api&work_ids%5B%5D=44275018"; const getWorkViews = async (workId) => { const response = await fetch(worksViewsPath); if (!response.ok) { throw new Error('Failed to load work views'); } const data = await response.json(); return data.views[workId]; }; // Get the view count for the work - we send this immediately rather than waiting for // the DOM to load, so it can be available as soon as possible (but without holding up // the backend or other resource requests, because it's a bit expensive and not critical). const viewCount = await getWorkViews(workId); const updateViewCount = (viewCount) => { try { const viewCountNumber = parseInt(viewCount, 10); if (viewCountNumber === 0) { // Remove the whole views element if there are zero views. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); return; } const commaizedViewCount = viewCountNumber.toLocaleString(); const viewCountBody = document.getElementById('work-metadata-view-count'); if (!viewCountBody) { throw new Error('Failed to find work views element'); } viewCountBody.textContent = `${commaizedViewCount} views`; } catch (error) { // Remove the whole views element if there was some issue parsing. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); throw new Error(`Failed to parse view count: ${viewCount}`, error); } }; // If the DOM is still loading, wait for it to be ready before updating the view count. if (document.readyState === "loading") { document.addEventListener('DOMContentLoaded', () => { updateViewCount(viewCount); }); // Otherwise, just update it immediately. } else { updateViewCount(viewCount); } })();</script></div><p class="ds-work-card--work-abstract ds-work-card--detail ds2-5-body-md">This monograph together with its complimentary volume [Siginer, D. A., Stability of Non-linear Constitutive Formulations for Viscoelastic Fluids, Springer, New York, 2014] in this series is an attempt to give an overall comprehensive view of a complex field, only 60 or so years old, still far from being settled on firm grounds, that of the dynamics of viscoelastic fluid flow and suspension flow in tubes. The monograph on “Stability of Non-linear Constitutive Formulations for Viscoelastic Fluid Media” covers the development of constitutive equation formulations for viscoelastic fluids in their historical context together with the latest progress made, and this volume covers the state-of-the-art knowledge in predicting the flow of viscoelastic fluids and suspensions in tubes highlighting the historical as well as the most recent findings. Most if not all viscoelastic fluids in industrial manufacturing processes flow in laminar regime through tubes, which are not necessarily circular, at one time or another during the processing of the material. Laminar regime is by far the predominant flow mode for viscoelastic fluids encountered in manufacturing processes, and it is extensively covered in this monograph. Turbulent flow of dilute viscoelastic solutions is a topic which has not received much attention except when related to drag reduction. For particle-laden flows there are very interesting developments in both laminar and turbulent regime, and they are duly covered. It is critically important that the flow of non-linear viscoelastic fluids and suspensions in tubes can be predicted on a sound basis, thus the raison d’eˆtre of this volume. As flow behavior predictions are directly related to the constitutive formulations used, this volume relies heavily on the volume on [Siginer, D. A., Stability of Non-linear Constitutive Formulations for Viscoelastic Fluids, Springer, New York, 2014]. The science of rheology defined as the study of the deformation and flow of matter was virtually single-handedly founded and the name invented by Professor Bingham of Lafayette College in the late 1920s. Rheology is a wide encompassing science which covers the study of the deformation and flow of diverse materials such as polymers, suspensions, asphalt, lubricants, paints, plastics, rubber, and biofluids, all of which display non-Newtonian behavior when subjected to external stimuli and as a result deform and flow in a manner not predictable by Newtonian mechanics. The development of rheology, which had gotten to a slow start, took a boost during WWII as materials used in various applications, in flame throwers, for instance, were found to be viscoelastic. As Truesdell and Noll famously wrote [Truesdell, C. and Noll, W., the Non-Linear Field Theories of Mechanics, 2nd ed., Springer, Berlin, 1992] “By 1949 all work on the foundations of Rheology done before 1945 had been rendered obsolete.” In the years following WWII, the emergence and rapid growth of the synthetic fiber and polymer processing industries, appearance of liquid detergents, multigrade oils, non-drip paints, and contact adhesives, and developments in pharmaceutical and food industries and biotechnology spurred the development of rheology. All these examples clearly illustrate the relevance of rheological studies to life and industry. The reliance of all these fields on rheological studies is at the very basis of many if not all of the amazing developments and success stories ending up with many of the products used by the public at large in everyday life. Non-Newtonian fluid mechanics, which is an integral part of rheology, really made big strides only after WWII and has been developing at a rapid rate ever since. The development of reliable constitutive formulations to predict the behavior of flowing substances with non-linear stress–strain relationships is quite a difficult proposition by comparison with Newtonian fluid mechanics with linear stress–strain relationship. The latter does enjoy a head start of two centuries tracing back its inception to Newton and luminaries like Euler and Bernoulli. With the former the non-linear structure does not allow the merging of the constitutive equations for the stress components with the linear momentum equation as it is the case with Newtonian fluids ending up with the Navier–Stokes equations. Thus, the practitioner ends up with six additional scalar equations to be solved in three dimensions for the six independent components of the symmetric stress tensor. The difficulties in solving in tandem this set of non-linear field equations, which may involve both inertial and constitutive non-linearities, cannot be underestimated. Perhaps equally importantly at this point in time in the unfolding development of the science, we are not fortunate enough to have developed a single constitutive formulation for viscoelastic fluids, which may lend itself to most applications and yield reasonably accurate predictions together with the field balance equations. The field is littered with a plethora of equations, some of which may yield reasonable predictions in some flows and utterly unacceptable predictions in others. Thus, we end up with classes of equations for viscoelastic fluids that would apply to classes of flows and fluids, an ad hoc concept at best that hopefully will give way one day to a universal equation, which may apply to all fluids in all motions. In addition the stability of these equations is a very important issue. Any given constitutive equation should be stable in the Hadamard and dissipative sense and should not violate the basic principles of thermodynamics. Dynamics of tube flow of non-Brownian suspensions and its underpinning field turbulent motion of linear (Newtonian) fluids shows interesting similarities with the flow of viscoelastic fluids in that the secondary flows of viscoelastic fluids in laminar flow driven by unbalanced normal stresses have a counterpart in the turbulent motion of linear fluids in straight tubes of non-circular cross section and in the laminar motion of particle-laden linear fluids. The latter secondary flows are driven by normal stresses due to shear-induced migration of particles. This is a new topic of hot research thrust given its implications in applications. The direction of these normal stresses is opposite of those present in the flow field of a viscoelastic fluid. In fact the tying thread among these seemingly different motions is that all are driven by normal stresses. The turbulent flow of linear fluids is known to have a transversal field due to the anisotropy of the Reynolds stress tensor in non-circular cross sections which entails unbalanced normal Reynolds stresses in the cross section perpendicular to the axial direction. Secondary field also exists in the turbulent flow of linear fluids in circular cross sections if the symmetry is somehow broken due, for example, to unevenly distributed roughness on the boundary, which would again trigger anisotropy of the Reynolds stress tensor. It is not possible to develop a good understanding of the mechanics of the secondary field both in laminar and turbulent motion of particle-laden fluids without a clear grasp of the underlying mechanics of the turbulent secondary field of homogeneous linear fluids. Thus a complete review of both is presented including interesting constitutive similarities with viscoelastic fluids which do arise when certain non-linear closure approximations are made for the anisotropic part of the Reynolds stress tensor. The impact of the secondary flows on engineering calculations is particularly important as turbulent flows in ducts of non-circular cross section are often encountered in engineering practice. Some examples are flows in heat exchangers, ventilation and air-conditioning systems, nuclear reactors, impellers, blade passages, aircraft intakes, and turbomachinery. If neglected significant errors may be introduced in the design as secondary flows lead to additional friction losses and can shift the location of the maximum momentum transport from the duct centerline. The secondary velocity depends on cross-sectional coordinates alone and therefore is independent of end effects. It is only of the order of 1–3 % of the streamwise bulk velocity, but by transporting high-momentum fluid toward the corners, it distorts substantially the cross-sectional equal axial velocity lines; specifically it causes a bulging of the velocity contours toward the corners with important consequences such as considerable friction losses. The need for turbulence models that can reliably predict the secondary flows that may occur in engineering applications is of paramount importance. Efforts have not been spared to be thorough in the presentation with commentaries about the successes and failures of each theory and the reasons behind them. The link between..... Palapye, Botswana and Santiago, Chile Dennis A. Siginer </p><div class="ds-work-card--button-container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--work-card","attachmentId":64652860,"attachmentType":"pdf","workUrl":"https://www.academia.edu/44275018/Developments_in_the_Flow_of_Complex_Fluids_in_Tubes"}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--work-card","attachmentId":64652860,"attachmentType":"pdf","workUrl":"https://www.academia.edu/44275018/Developments_in_the_Flow_of_Complex_Fluids_in_Tubes"}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div></div><div data-auto_select="false" data-client_id="331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b" data-doc_id="64652860" data-landing_url="https://www.academia.edu/44275018/Developments_in_the_Flow_of_Complex_Fluids_in_Tubes" data-login_uri="https://www.academia.edu/registrations/google_one_tap" data-moment_callback="onGoogleOneTapEvent" id="g_id_onload"></div><div class="ds-top-related-works--grid-container"><div class="ds-related-content--container ds-top-related-works--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="0" data-entity-id="19261498" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/19261498/NON_NEWTONIAN_FLOW_AND_APPLIED_RHEOLOGY">NON NEWTONIAN FLOW AND APPLIED RHEOLOGY</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="21478104" href="https://hhu.academia.edu/DrBINAMAMaxime">Dr. Binama Maxime</a></div><p class="ds-related-work--abstract ds2-5-body-sm">Non-Newtonian fl ow and rheology are subjects which are essentially interdisciplinary in their nature and which are also wide in their areas of application. Indeed non-Newtonian fl uid behaviour is encountered in almost all the chemical and allied processing industries. The factors which determine the rheological characteristics of a material are highly complex, and their full understanding necessitates a contribution from physicists, chemists and applied mathematicians, amongst others, few of whom may have regarded the subject as central to their disciplines. Furthermore, the areas of application are also extremely broad and diverse, and require an important input from engineers with a wide range of backgrounds, though chemical and process engineers, by virtue of their role in the handling and processing of complex materials (such as foams, slurries, emulsions, polymer melts and solutions, etc.), have a dominant interest. Furthermore, the subject is of interest both to highly theoretical mathematicians and scientists and to practising engineers with very different cultural backgrounds.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"NON NEWTONIAN FLOW AND APPLIED RHEOLOGY","attachmentId":40522091,"attachmentType":"pdf","work_url":"https://www.academia.edu/19261498/NON_NEWTONIAN_FLOW_AND_APPLIED_RHEOLOGY","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/19261498/NON_NEWTONIAN_FLOW_AND_APPLIED_RHEOLOGY"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="1" data-entity-id="14974206" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/14974206/On_the_fully_developed_tube_flow_of_a_class_of_non_linear_viscoelastic_fluids">On the fully developed tube flow of a class of non-linear viscoelastic fluids</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="33969261" href="https://usach.academia.edu/DennisSiginer">Dennis A . Siginer</a></div><p class="ds-related-work--metadata ds2-5-body-xs">International Journal of Non-Linear Mechanics, 2005</p><p class="ds-related-work--abstract ds2-5-body-sm">The fully developed pipe ﬂow of a class of non-linear viscoelastic ﬂuids is investigated. Analytical expressions are derived for the stress components, the friction factor and the velocity ﬁeld. The friction factor which depends on the Deborah and Reynolds numbers is substantially smaller than the corresponding value for the Newtonian ﬂow ﬁeld with implications concerning the volume ﬂow rate. We show that non-afﬁne models in the class of constitutive equations considered such as Johnson–Segalman and some versions of the Phan–Thien–Tanner models are not representative of physically realistic ﬂow ﬁelds for all Deborah numbers. For a ﬁxed value of the slippage factor they predict physically admissible ﬂow ﬁelds only for a limited range of Deborah numbers smaller than a critical Deborah number. The latter is a function of the slippage.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On the fully developed tube flow of a class of non-linear viscoelastic fluids","attachmentId":41047999,"attachmentType":"pdf","work_url":"https://www.academia.edu/14974206/On_the_fully_developed_tube_flow_of_a_class_of_non_linear_viscoelastic_fluids","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/14974206/On_the_fully_developed_tube_flow_of_a_class_of_non_linear_viscoelastic_fluids"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="2" data-entity-id="86787256" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/86787256/Nonlinear_effects_in_the_unsteady_flow_of_viscoelastic_fluids">Nonlinear effects in the unsteady flow of viscoelastic fluids</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="108114053" href="https://independent.academia.edu/CharlesGoldstein1">Charles Goldstein</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Rheologica Acta, 1973</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Nonlinear effects in the unsteady flow of viscoelastic fluids","attachmentId":91163391,"attachmentType":"pdf","work_url":"https://www.academia.edu/86787256/Nonlinear_effects_in_the_unsteady_flow_of_viscoelastic_fluids","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/86787256/Nonlinear_effects_in_the_unsteady_flow_of_viscoelastic_fluids"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="3" data-entity-id="111548950" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/111548950/Modifications_to_Non_linear_Rheological_Models_of_Viscoelastic_Fluids">Modifications to Non-linear Rheological Models of Viscoelastic Fluids</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="287086239" href="https://independent.academia.edu/MuhamadAbdureza">Muhamad Abdu reza</a></div><p class="ds-related-work--abstract ds2-5-body-sm">Four constitutive equations have been used to describe the behaviour of viscoelastic fluids viz., (i) upper convectedMaxwell, (ii) Oldroyd 4-constant, (iii) Bogue-White and (iv) Bird-Carreau . These were modified to improve their ability to predict the observed behaviour of viscoelastic fluids in viscometric and oscillatory shear flows. The fluids used during the experimental work are four different concentrations ofpolyacrylamide (SeparanAP 30) solutions, i.e. 0.6, 0.8, 1.0, and 1.2%, in glycerine I water mixtures. The experimental data are obtained under simple shear and small-amplitude oscillatory shear flow conditions. The viscosity data, obtained fromsteady shear experiments, and the dynamic viscosity and storage modulus obtained from oscillatory shear experiments have been used to determine the model parameters . The performance of the original and modified models have been studied by comparing their predictions of the viscosities, in steady, and the dynamic viscosities, in os...</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Modifications to Non-linear Rheological Models of Viscoelastic Fluids","attachmentId":109055976,"attachmentType":"pdf","work_url":"https://www.academia.edu/111548950/Modifications_to_Non_linear_Rheological_Models_of_Viscoelastic_Fluids","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/111548950/Modifications_to_Non_linear_Rheological_Models_of_Viscoelastic_Fluids"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="4" data-entity-id="117249900" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/117249900/Isothermal_tube_flow_of_non_linear_viscoelastic_fluids_Part_II_Transversal_field">Isothermal tube flow of non-linear viscoelastic fluids. Part II: Transversal field</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="33969261" href="https://usach.academia.edu/DennisSiginer">Dennis A . Siginer</a></div><p class="ds-related-work--metadata ds2-5-body-xs">International Journal of Engineering Science, 2011</p><p class="ds-related-work--abstract ds2-5-body-sm">Theories and attendant methodologies developed independently of thermodynamic considerations and set within a thermodynamic framework to derive rheological constitutive equations for viscoelastic fluids have been reviewed in their historical context. The stability of Maxwell-like differential and single integral type constitutive formulations in current use and their relationship to experimentally observed physical instabilities are reviewed in particular in the light of inherent Hadamard and dissipative type of instabilities they may be subject to as a consequence of defective constitutive formulations. The state of the art in predicting the longitudinal field, the pressure drop and the friction factors for the flow of generalized Newtonian and viscoelastic fluids in circular and non-circular straight tubes is reviewed.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Isothermal tube flow of non-linear viscoelastic fluids. Part II: Transversal field","attachmentId":113156657,"attachmentType":"pdf","work_url":"https://www.academia.edu/117249900/Isothermal_tube_flow_of_non_linear_viscoelastic_fluids_Part_II_Transversal_field","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/117249900/Isothermal_tube_flow_of_non_linear_viscoelastic_fluids_Part_II_Transversal_field"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="5" data-entity-id="35948916" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/35948916/Isothermal_Tube_Flow_of_Non_Linear_Viscoelastic_Fluids_Part_I_Constitutive_Instabilities_and_the_Longitudinal_Field">Isothermal Tube Flow of Non-Linear Viscoelastic Fluids, Part I: Constitutive Instabilities and the Longitudinal Field</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="33969261" href="https://usach.academia.edu/DennisSiginer">Dennis A . Siginer</a></div><p class="ds-related-work--metadata ds2-5-body-xs">International Journal of Engineering Science 56:111-126, 2012, 2012</p><p class="ds-related-work--abstract ds2-5-body-sm">Theories and attendant methodologies developed independently of thermodynamic considerations and set within a thermodynamic framework to derive rheological constitutive equations for viscoelastic fluids have been reviewed in their historical context. The stability of Maxwell-like differential and single integral type constitutive formulations in current use and their relationship to experimentally observed physical instabilities are reviewed in particular in the light of inherent Hadamard and dissipative type of instabilities they may be subject to as a consequence of defective constitutive formulations. The state of the art in predicting the longitudinal field, the pressure drop and the friction factors for the flow of generalized Newtonian and viscoelastic fluids in circular and non-circular straight tubes is reviewed.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Isothermal Tube Flow of Non-Linear Viscoelastic Fluids, Part I: Constitutive Instabilities and the Longitudinal Field","attachmentId":55831547,"attachmentType":"pdf","work_url":"https://www.academia.edu/35948916/Isothermal_Tube_Flow_of_Non_Linear_Viscoelastic_Fluids_Part_I_Constitutive_Instabilities_and_the_Longitudinal_Field","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/35948916/Isothermal_Tube_Flow_of_Non_Linear_Viscoelastic_Fluids_Part_I_Constitutive_Instabilities_and_the_Longitudinal_Field"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="35950500" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/35950500/Erratum_Laminar_flow_of_non_linear_viscoelastic_fluids_in_straight_tubes_of_arbitrary_contour_International_Journal_of_Heat_and_Mass_Transfer_2011_54_2188_2202_">Erratum: Laminar flow of non-linear viscoelastic fluids in straight tubes of arbitrary contour (International Journal of Heat and Mass Transfer (2011) 54 (2188-2202))</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="33969261" href="https://usach.academia.edu/DennisSiginer">Dennis A . Siginer</a></div><p class="ds-related-work--metadata ds2-5-body-xs">International Journal of Heat and Mass Transfer 55 (2012) 2731–2745, 2012</p><p class="ds-related-work--abstract ds2-5-body-sm">The fully developed steady velocity field in pressure gradient driven laminar flow of non-linear viscoelas-tic fluids with instantaneous elasticity constitutively represented by a class of single mode, non-affine quasilinear constitutive equations is investigated in straight pipes of arbitrary contour. A continuous one-to-one mapping is used to obtain arbitrary tube contours from a base tube contour. The analytical method presented is capable of predicting the velocity field in tubes with arbitrary cross-section. The base flow is the Newtonian field and is obtained at O(1). Field variables are expanded in asymptotic series in terms of the Weissenberg number Wi. The analysis does not place any restrictions on the smallness of the driving pressure gradients which can be large and applies to dilute and weakly elastic non-linear vis-coelastic fluids. The velocity field is investigated up to and including the third order in Wi. The Newtonian field in general arbitrary contours is obtained and longitudinal velocity field components due to shear-thinning and to non-linear viscoelastic effects are identified. Third order analysis shows a further contribution to the longitudinal field driven by first normal stress differences. Secondary flows driven by unbalanced second normal stresses in the cross-section manifest themselves as well at this order. Longitudinal equal velocity contours, the secondary flow field structure, the first and the second normal stress differences as well as wall shear stress variations are discussed for several non-circular contours some for the first time.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Erratum: Laminar flow of non-linear viscoelastic fluids in straight tubes of arbitrary contour (International Journal of Heat and Mass Transfer (2011) 54 (2188-2202))","attachmentId":55833379,"attachmentType":"pdf","work_url":"https://www.academia.edu/35950500/Erratum_Laminar_flow_of_non_linear_viscoelastic_fluids_in_straight_tubes_of_arbitrary_contour_International_Journal_of_Heat_and_Mass_Transfer_2011_54_2188_2202_","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/35950500/Erratum_Laminar_flow_of_non_linear_viscoelastic_fluids_in_straight_tubes_of_arbitrary_contour_International_Journal_of_Heat_and_Mass_Transfer_2011_54_2188_2202_"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="125796194" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/125796194/Recent_Advances_in_Mechanics_of_Non_Newtonian_Fluids">Recent Advances in Mechanics of Non-Newtonian Fluids</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="13011917" href="https://cmu.academia.edu/MehrdadMassoudi">Mehrdad Massoudi</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Fluids, 2020</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Recent Advances in Mechanics of Non-Newtonian Fluids","attachmentId":119774254,"attachmentType":"pdf","work_url":"https://www.academia.edu/125796194/Recent_Advances_in_Mechanics_of_Non_Newtonian_Fluids","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/125796194/Recent_Advances_in_Mechanics_of_Non_Newtonian_Fluids"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="120868399" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/120868399/Comments_on_the_paper_by_M_F_Letelier_and_D_A_Siginer_On_the_flow_of_a_class_of_viscoinelastic_viscoplastic_fluids_in_tubes_of_non_circular_contour_International_Journal_of_Engineering_Science_Vol_45_2007_873_881">Comments on the paper by M. F. Letelier and D. A. Siginer : On the flow of a class of viscoinelastic–viscoplastic fluids in tubes of non-circular contour. International Journal of Engineering Science, Vol. 45 (2007), 873–881</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="306091472" href="https://independent.academia.edu/RajaHuilgol">Raja Huilgol</a></div><p class="ds-related-work--metadata ds2-5-body-xs">International Journal of Engineering Science, 2018</p><p class="ds-related-work--abstract ds2-5-body-sm">It is shown that the solution to the steady flow of a Newtonian fluid in a pipe of equilateral triangular cross-section is wrong, for it is based on an inappropriate choice of a parameter and the incorrect use of trigonometry. Secondly, the assumption that the shear stresses in a steady flow in a pipe are given by the gradient of a scalar function is also incorrect, since it depends on the equality between directional and partial derivatives everywhere.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Comments on the paper by M. F. Letelier and D. A. Siginer : On the flow of a class of viscoinelastic–viscoplastic fluids in tubes of non-circular contour. International Journal of Engineering Science, Vol. 45 (2007), 873–881","attachmentId":115884835,"attachmentType":"pdf","work_url":"https://www.academia.edu/120868399/Comments_on_the_paper_by_M_F_Letelier_and_D_A_Siginer_On_the_flow_of_a_class_of_viscoinelastic_viscoplastic_fluids_in_tubes_of_non_circular_contour_International_Journal_of_Engineering_Science_Vol_45_2007_873_881","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/120868399/Comments_on_the_paper_by_M_F_Letelier_and_D_A_Siginer_On_the_flow_of_a_class_of_viscoinelastic_viscoplastic_fluids_in_tubes_of_non_circular_contour_International_Journal_of_Engineering_Science_Vol_45_2007_873_881"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="33472282" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/33472282/Transition_to_turbulence_in_pipe_flow_of_Newtonian_and_Non_Newtonian_fluids">Transition to turbulence in pipe flow of Newtonian and Non Newtonian fluids</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="292212" href="https://umn.academia.edu/DevranjanSamanta">Devranjan Samanta</a></div><p class="ds-related-work--abstract ds2-5-body-sm">English: Experimental investigations were carried out in pipe flow of Newtonian and Non Newtonian fluids. The investigations of Newtonian flow were focused on the origin of laminar turbulent intermittency in the flow. It was found that upon reduction of the Reynolds number starting from fully turbulent flows laminar regions appear randomly. Unlike reported for other shear flows there was no wavelength induced instability in pipe flow. The development of intermittent patterns and in particular the minimum spacing between turbulent puffs is shown as a consequence of an interaction between neighboring puffs which has been identified. The puff interaction distance is found to decrease with increase in Re and it is in quantitative agreement with minimum spacing of plane Couette and Taylor Couette flow.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Transition to turbulence in pipe flow of Newtonian and Non Newtonian fluids","attachmentId":53516401,"attachmentType":"pdf","work_url":"https://www.academia.edu/33472282/Transition_to_turbulence_in_pipe_flow_of_Newtonian_and_Non_Newtonian_fluids","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/33472282/Transition_to_turbulence_in_pipe_flow_of_Newtonian_and_Non_Newtonian_fluids"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":64652860,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":64652860,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_64652860" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. 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Pérez-segarra</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Numerical Heat Transfer, Part B: Fundamentals, 2015</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Numerical Analysis of the Transpose Diffusive Term for Viscoplastic-Type Non-Newtonian Fluid Flows Using a Collocated Variable Arrangement","attachmentId":72468446,"attachmentType":"pdf","work_url":"https://www.academia.edu/57690907/Numerical_Analysis_of_the_Transpose_Diffusive_Term_for_Viscoplastic_Type_Non_Newtonian_Fluid_Flows_Using_a_Collocated_Variable_Arrangement","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/57690907/Numerical_Analysis_of_the_Transpose_Diffusive_Term_for_Viscoplastic_Type_Non_Newtonian_Fluid_Flows_Using_a_Collocated_Variable_Arrangement"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="8" data-entity-id="95558873" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/95558873/Velocity_distributions_and_normal_stresses_in_viscoelastic_turbulent_pipe_flow">Velocity distributions and normal stresses in viscoelastic turbulent pipe flow</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="22941053" href="https://salerno.academia.edu/LuigiNicodemo">Luigi Nicodemo</a></div><p class="ds-related-work--metadata ds2-5-body-xs">AIChE Journal, 1966</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Velocity distributions and normal stresses in viscoelastic turbulent pipe flow","attachmentId":97706924,"attachmentType":"pdf","work_url":"https://www.academia.edu/95558873/Velocity_distributions_and_normal_stresses_in_viscoelastic_turbulent_pipe_flow","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/95558873/Velocity_distributions_and_normal_stresses_in_viscoelastic_turbulent_pipe_flow"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="9" data-entity-id="20175122" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/20175122/Secondary_flows_of_viscoelastic_liquids_in_straight_tubes">Secondary flows of viscoelastic liquids in straight tubes</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="33969261" href="https://usach.academia.edu/DennisSiginer">Dennis A . 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Siginer</a></div><p class="ds-related-work--metadata ds2-5-body-xs">International Journal of Heat and Mass Transfer, 2011</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Laminar flow of non-linear viscoelastic fluids in straight tubes of arbitrary contour","attachmentId":43684688,"attachmentType":"pdf","work_url":"https://www.academia.edu/14974151/Laminar_flow_of_non_linear_viscoelastic_fluids_in_straight_tubes_of_arbitrary_contour","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/14974151/Laminar_flow_of_non_linear_viscoelastic_fluids_in_straight_tubes_of_arbitrary_contour"><span 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class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="2022765" href="https://bgu.academia.edu/ChaimElata">Chaim Elata</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Rheologica Acta, 1968</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On the stability of elastico-viscous flows","attachmentId":77059701,"attachmentType":"pdf","work_url":"https://www.academia.edu/65483345/On_the_stability_of_elastico_viscous_flows","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/65483345/On_the_stability_of_elastico_viscous_flows"><span 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Cardozo</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Non-Newtonian Fluid Mechanics, 2010</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Viscoelastic flow analysis using the software OpenFOAM and differential constitutive equations","attachmentId":48004496,"attachmentType":"pdf","work_url":"https://www.academia.edu/27734852/Viscoelastic_flow_analysis_using_the_software_OpenFOAM_and_differential_constitutive_equations","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" 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