Journal of Non-Newtonian Fluid Mechanics最新文献

{"title":"Pressure drop reduction due to coupling between shear-thinning fluid flow and a weakly deformable channel wall: A reciprocal theorem approach","authors":"Shrihari D. Pande,&nbsp;Ivan C. Christov","doi":"10.1016/j.jnnfm.2024.105347","DOIUrl":"10.1016/j.jnnfm.2024.105347","url":null,"abstract":"<div><div>We employ the Lorentz reciprocal theorem to derive a closed-form expression for the pressure drop reduction due to the coupling between shear-thinning fluid flow and a weakly deformable channel wall in terms of the shear rate and the viscosity function (and its derivative) of the underlying rigid-channel flow. The methodology is applied in parallel to fluids for which the generalized Newtonian viscosity depends on either the shear rate or the shear stress magnitude. When the viscosity model allows for a closed-form solution for the axial velocity profile in a straight and rigid channel, the pressure drop reduction can be evaluated in closed form, which we demonstrate for the power-law and Ellis viscosity models as featured examples and to enable comparisons to previous works. Importantly, the pressure drop reduction under the Ellis model is valid for both small and large Carreau (or Ellis) numbers, and we show that it reduces to the analytical expression under the power-law model for large Carreau (small Ellis) numbers.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"335 ","pages":"Article 105347"},"PeriodicalIF":2.7,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Flow enhancement produced by a pulsatile flow of shear-thinning fluids in circular and concentric annular tubes","authors":"J. Báez-Amador ,&nbsp;R. Baños ,&nbsp;J. Arcos ,&nbsp;F. Méndez ,&nbsp;O. Bautista","doi":"10.1016/j.jnnfm.2024.105346","DOIUrl":"10.1016/j.jnnfm.2024.105346","url":null,"abstract":"<div><div>Although the analysis of the flow enhancement of non-Newtonian fluids produced by pulsatile flows through tubes is common in the literature, the case of Carreau fluid has not been analyzed, which is the aim of this work. This study determines the flow enhancement caused by the pulsatile fluid flow through <strong>(a)</strong> a circular tube and <strong>(b)</strong> a concentric annular tube. We show that the flow rate enhancement of the shear-thinning fluid is controlled by the Carreau number <span><math><mrow><mi>C</mi><mi>u</mi></mrow></math></span>, the Womersley number <span><math><mrow><mi>W</mi><mi>o</mi></mrow></math></span>, the fluid power-law index <span><math><mi>n</mi></math></span>, the ratio between the outer and inner radii <span><math><mi>κ</mi></math></span>, a parameter <span><math><mi>β</mi></math></span> that represents the ratio between the infinite and zero-shear viscosities, and the amplitude of the oscillatory signal <span><math><mi>ɛ</mi></math></span>. In both cases <strong>(a)</strong> and <strong>(b)</strong>, a numerical solution of the start-up of the hydrodynamic is evaluated. With the aid of the velocity solution, the volumetric flow rate is determined under periodic conditions after the initial transient has vanished. Then, the fractional increase in the mean flow rate <span><math><mi>I</mi></math></span> due to the pulsatile pressure gradient is calculated. Furthermore, an asymptotic solution for small, intermediate, and very large values of the Carreau number is performed to provide physical insight into flow enhancement.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"334 ","pages":"Article 105346"},"PeriodicalIF":2.7,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142571410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A fully-coupled implementation of the contravariant deformation tensor formulation for viscoelastic flows","authors":"Nick O. Jaensson,&nbsp;Martien A. Hulsen","doi":"10.1016/j.jnnfm.2024.105345","DOIUrl":"10.1016/j.jnnfm.2024.105345","url":null,"abstract":"<div><div>We present a fully-coupled numerical scheme for computing steady and time-dependent viscoelastic flows. The scheme relies on the contravariant deformation tensor formulation and uses a Newton–Raphson iteration to solve the non-linear system of equations. The contravariant reformulation allows for the computation and implementation of the analytical Jacobian relatively easily, especially compared to other reformulations such as the log-conformation. The contravariant deformation tensor rotates in steady state shearing flows, which is solved here by “resetting” it as a pre-processing step in the numerical scheme, rather than a post-processing step. We use the finite element method with standard stabilization techniques (SUPG and DEVSS-G) for the spatial discretization. The numerical scheme is tested in three viscoelastic flow problems which are studied in terms of stability and accuracy: planar Couette flow, 2D flow around a cylinder and 3D flow around a sphere. For all problems, quadratic convergence is observed in both the difference between iterations and the residuals during the Newton–Raphson procedure. Moreover, we observe that the residuals are several orders smaller than the difference between iterations. A distinct advantage of the numerical scheme presented here, is that it significantly relaxes the requirement on the time-step size in time-dependent problems, as compared to explicit or semi-implicit methods. Moreover, steady states can be efficiently computed if the initial guess in the Newton–Raphson iteration is close enough to the solution.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"334 ","pages":"Article 105345"},"PeriodicalIF":2.7,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142571409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Slot coating of time-dependent structured materials: Effects of thixotropy on the flow dynamics and operating limits","authors":"C. Sanchez-Perez,&nbsp;D. Maza,&nbsp;I.R. Siqueira,&nbsp;P.R. de Souza Mendes,&nbsp;M.S. Carvalho","doi":"10.1016/j.jnnfm.2024.105344","DOIUrl":"10.1016/j.jnnfm.2024.105344","url":null,"abstract":"<div><div>Some of the most common liquid-like formulations rooted in the coating industry consist of rheologically complex structured materials such as inks, paints, and slurries. Yet, the impact of time-dependent structuring effects due to thixotropy on thin film coating applications remains elusive and still unclear. Here, we present a computational study of the effects of thixotropy on slot coating of time-dependent structured materials. By coupling a recent fluidity-based constitutive model for thixotropic materials with a well-established finite element/elliptic mesh generation method for free surface flows, we assess the role of thixotropy by comparing the predictions from the thixotropic model with those from a simple Generalized Newtonian Fluid model that uses the same flow curve for the material steady-state equilibrium viscosity. We find that thixotropy can indeed have a major impact on slot coating applications, potentially bringing strong implications not only to the flow dynamics but also to the operating limits of the process. In conclusion, the results and discussions we present in this study underscore the importance of accounting for thixotropy to genuinely model and fundamentally understand the behavior of time-dependent structured materials with complex rheology in processing flows like those ubiquitous across the broad fields of coating science and engineering.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"334 ","pages":"Article 105344"},"PeriodicalIF":2.7,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142551993","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analytic solution for the linear rheology of living polymers","authors":"Vickie Chen ,&nbsp;Charles T. Drucker ,&nbsp;Claire Love ,&nbsp;Jonathon Peterson ,&nbsp;Joseph D. Peterson","doi":"10.1016/j.jnnfm.2024.105343","DOIUrl":"10.1016/j.jnnfm.2024.105343","url":null,"abstract":"<div><div>It is often said that well-entangled and fast-breaking living polymers (such as wormlike micelles) exhibit a single relaxation time in their reptation dynamics, but the full story is somewhat more complicated. Understanding departures from single-Maxwell behavior is crucial for fitting and interpreting experimental data, but in some limiting cases numerical methods for solving living polymer models can struggle to produce reliable predictions/interpretations. In this work, we develop an analytic solution for the shuffling model of living polymers. The analytic solution is a converging infinite series, and it converges fastest in the fast-breaking limit where other methods can struggle.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"334 ","pages":"Article 105343"},"PeriodicalIF":2.7,"publicationDate":"2024-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142526219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The motion of a self-propelling two-sphere swimmer in a weakly viscoelastic fluid","authors":"Mary Agnes Joens ,&nbsp;Patrick S. Doyle ,&nbsp;Gareth H. McKinley","doi":"10.1016/j.jnnfm.2024.105330","DOIUrl":"10.1016/j.jnnfm.2024.105330","url":null,"abstract":"<div><div>We study analytically the propulsion of a force- and torque-free swimmer composed of two counterrotating spheres of differing radii through a viscoelastic fluid described by the Giesekus constitutive model. Our analysis includes both swimmers composed of directly touching spheres and those composed of spheres separated by some finite distance. The propulsion speed of the swimmer is calculated by first expanding the equations of motion and the Giesekus constitutive model as a power series in the Weissenberg number, and then using the Lorentz reciprocal theorem to determine the first-order propulsion speed using the known flow fields for rotating and translating two-sphere geometries at zeroth order. We calculate the relative rotation speeds of the two spheres necessary to maintain the torque-free condition, including an approximate correction for fluid elasticity. The impact of the separation distance between the two spheres, the ratio of their radii, and the value of the Giesekus mobility parameter <span><math><mi>α</mi></math></span> on the propulsion speed are all examined; we find that the propulsion speed of the swimmer is maximized for two touching spheres with a radius ratio of approximately 0.7, with a Giesekus mobility parameter of <span><math><mrow><mi>α</mi><mo>=</mo><mn>0</mn></mrow></math></span>, corresponding to an Oldroyd-B fluid. We also quantify how increased shear-thinning in the fluid, represented by increasing values of <span><math><mi>α</mi></math></span>, results in a significant decrease in the swimmer speed. Finally, through calculations of the fluid stresses around the two-sphere swimmer, we demonstrate the development of enhanced hoop stresses around the smaller sphere, which drive the expulsion of stretched fluid behind the smaller sphere and induce motion of the swimmer in the direction of the larger sphere.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"334 ","pages":"Article 105330"},"PeriodicalIF":2.7,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142551992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A revisit of the development of viscoplastic flow in pipes and channels","authors":"Alexandros Syrakos ,&nbsp;Evgenios Gryparis ,&nbsp;Georgios C. Georgiou","doi":"10.1016/j.jnnfm.2024.105341","DOIUrl":"10.1016/j.jnnfm.2024.105341","url":null,"abstract":"<div><div>This study revisits the development of viscoplastic flow in pipes and channels, focusing on the flow of a Bingham plastic. Using finite element simulations and the Papanastasiou regularisation, results are obtained across a range of Reynolds and Bingham numbers. The novel contributions of this work include: (a) investigating a definition of the development length based on wall shear stress, a critical parameter in numerous applications; (b) considering alternative definitions of the Reynolds number in an effort to collapse the development length curves onto a single master curve, independent of the Bingham number; (c) examining the patterns of yielded and unyielded regions within the flow domain; and (d) assessing the impact of the regularisation parameter on the accuracy of the results. The findings enhance the existing literature, providing a more comprehensive understanding of this classic flow problem.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"334 ","pages":"Article 105341"},"PeriodicalIF":2.7,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142437779","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An exact solution of the lubrication equations for the Oldroyd-B model in a hyperbolic pipe","authors":"Panagiotis Sialmas,&nbsp;Kostas D. Housiadas","doi":"10.1016/j.jnnfm.2024.105331","DOIUrl":"10.1016/j.jnnfm.2024.105331","url":null,"abstract":"<div><div>An exact analytical solution of the lubrication equations for the steady, isothermal, incompressible flow of a viscoelastic Oldroyd-B fluid in a hyperbolic cylindrical contracting pipe is derived. The solution is valid for values of the Deborah number, De, up to order unity (De is defined as the ratio of the longest relaxation time of the polymer to the characteristic residence time of the fluid in the pipe), all values of the ratio of the polymer viscosity to the total viscosity of the fluid, η, and typical values of the contraction ratio, Λ, encountered in experiments and practical applications. It is provided in terms of the streamfunction only and is used in the momentum balance to derive a strongly non-linear ordinary differential equation of second order with unknown a function which corresponds to a modified fluid velocity along the main flow direction. The final equation is solved semi-numerically using a fully spectral (Legendre)-Galerkin approach to resolve the unknown function almost down to machine accuracy. The exact solution for the polymer extra-stresses, which is emphasized is not the full solution of the complete lubrication equations, allows for the derivation of a variety of theoretical expressions for the average pressure-drop along the pipe. In all cases, a decrease in the pressure drop compared to the Newtonian value with increasing De, η and/or Λ is predicted. The differences between the corresponding analytical solution for the planar geometrical configuration are also identified and discussed.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"335 ","pages":"Article 105331"},"PeriodicalIF":2.7,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Master curves for unidirectional flows of FENE-P fluids in rectilinear and curvilinear geometries","authors":"P.S.D. Surya Phani Tej ,&nbsp;Pratyush Kumar Mohanty ,&nbsp;V. Shankar","doi":"10.1016/j.jnnfm.2024.105332","DOIUrl":"10.1016/j.jnnfm.2024.105332","url":null,"abstract":"<div><div>We demonstrate that velocity profiles for steady, unidirectional shear flows of the FENE-P (Finitely-Extensible Nonlinear Elastic, with Peterlin closure) fluid, undergoing canonical rectilinear (pressure-driven flow in a rectangular channel or a circular pipe) or curvilinear (in Taylor–Couette or Dean configurations) flows, obey universal master curves that are a function only of the ratio <span><math><mrow><mi>W</mi><mspace></mspace><mi>i</mi><mo>/</mo><mi>L</mi></mrow></math></span> , for a fixed solvent to solution viscosity parameter <span><math><mi>β</mi></math></span>. Here, <span><math><mrow><mi>W</mi><mspace></mspace><mi>i</mi></mrow></math></span> is the Weissenberg number defined as the product of the dumbbell relaxation time and an appropriate shear rate, while <span><math><mi>L</mi></math></span> is the ratio of the maximum extension of the polymer to its equilibrium root-mean-square end-to-end distance. The data collapse and the resulting master curves for the velocity profile is a generalization of the recent demonstration of master curves for polymer viscosity and first normal stress coefficient for a FENE-P fluid under steady simple shear flow (Yamani and McKinley, 2023). For pressure-driven channel and pipe flows, we derive simple analytical expressions for the velocity profiles, in the high shear-rate regime of <span><math><mrow><mi>W</mi><mspace></mspace><mi>i</mi><mo>/</mo><mi>L</mi><mo>≫</mo><mn>1</mn></mrow></math></span>, that readily elucidate the role of finite extensibility of the polymer on the velocity profiles. In the <span><math><mrow><mi>W</mi><mspace></mspace><mi>i</mi><mo>/</mo><mi>L</mi><mo>≫</mo><mn>1</mn></mrow></math></span> regime, for all the flows considered, the limit of zero solvent (<span><math><mrow><mi>β</mi><mo>=</mo><mn>0</mn></mrow></math></span>) is shown to be singular, owing to the absence of a high-shear plateau in the total solution viscosity, resulting in very different velocity profiles for <span><math><mrow><mi>β</mi><mo>=</mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mi>β</mi><mo>→</mo><mn>0</mn></mrow></math></span>.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"334 ","pages":"Article 105332"},"PeriodicalIF":2.7,"publicationDate":"2024-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142417119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stokes layers in complex fluids","authors":"D.R. Hewitt ,&nbsp;N.J. Balmforth","doi":"10.1016/j.jnnfm.2024.105328","DOIUrl":"10.1016/j.jnnfm.2024.105328","url":null,"abstract":"<div><div>Stokes’s second problem is reconsidered for three models of complex fluids: an elasto-viscoplastic fluid, a thixotropic viscoplastic fluid and a discontinuously shear-thickening fluid. In each case, the Stokes-layer dynamics is interrogated with a view to examining the signatures of the detailed rheology. Significant deformations are possible below the yield stress for elasto-viscoplastic fluids as a result of the excitation of elastic waves, particularly near resonances. Thixotropic fluids with viscosity bifurcations layer internally, but surface-speed signatures mostly appear similar to those for simple yield-stress fluids. Stokes-layer oscillations of discontinuous shear thickening fluids can prompt abrupt increases in viscosity, introducing sudden jumps in surface speed. Pre-existing experimental results for layers of kaolin slurries in a motorized, oscillating tray are reconsidered and compared with the results for elasto-viscoplastic and thixotropic fluids.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"334 ","pages":"Article 105328"},"PeriodicalIF":2.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142417121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}