Pub Date : 2025-07-21DOI: 10.1016/j.jnnfm.2025.105459
Miguel Beneitez , Soufiane Mrini , Rich R. Kerswell
Elastic turbulence has been found in computations of planar viscoelastic Taylor–Couette flow using the Oldroyd-B model, apparently generated by a linear instability van Buel et al. (2018). We demonstrate that no such linear instability exists in the governing equations used unless some diffusion is added to the polymer conformation tensor equation, as might occur through a diffusive numerical scheme. With this addition, the polymer diffusive instability (PDI) Beneitez et al. (2023) exists and leads to chaotic flows resembling those found by van Buel et al. (2018). We show how finite volume or finite-difference discretisations of the governing equations can naturally introduce diffusive errors near boundaries which are sufficient to trigger PDI. This suggests that PDI could well be important in numerical solutions of wall-bounded viscoelastic flows modelled using Oldroyd-B and FENE-P even with no polymer stress diffusion explicitly included.
在使用Oldroyd-B模型计算平面粘弹性Taylor-Couette流时发现了弹性湍流，这显然是由线性不稳定性van Buel等人（2018）产生的。我们证明，除非在聚合物构象张量方程中加入一些扩散，否则在所使用的控制方程中不存在这种线性不稳定性，这可能通过扩散数值格式发生。有了这个补充，聚合物扩散不稳定性（PDI） Beneitez et al.（2023）存在，并导致类似于van Buel et al.（2018）发现的混沌流动。我们展示了控制方程的有限体积或有限差分离散如何自然地在边界附近引入足以触发PDI的扩散误差。这表明，即使没有明确包括聚合物应力扩散，PDI在使用Oldroyd-B和FENE-P模拟的壁面粘弹性流动的数值解中也很重要。
{"title":"Linear instability in planar viscoelastic Taylor–Couette flow with and without explicit polymer diffusion","authors":"Miguel Beneitez , Soufiane Mrini , Rich R. Kerswell","doi":"10.1016/j.jnnfm.2025.105459","DOIUrl":"10.1016/j.jnnfm.2025.105459","url":null,"abstract":"<div><div>Elastic turbulence has been found in computations of planar viscoelastic Taylor–Couette flow using the Oldroyd-B model, apparently generated by a linear instability van Buel et al. (2018). We demonstrate that no such linear instability exists in the governing equations used unless some diffusion is added to the polymer conformation tensor equation, as might occur through a diffusive numerical scheme. With this addition, the polymer diffusive instability (PDI) Beneitez et al. (2023) exists and leads to chaotic flows resembling those found by van Buel et al. (2018). We show how finite volume or finite-difference discretisations of the governing equations can naturally introduce diffusive errors near boundaries which are sufficient to trigger PDI. This suggests that PDI could well be important in numerical solutions of wall-bounded viscoelastic flows modelled using Oldroyd-B and FENE-P even with no polymer stress diffusion explicitly included.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"345 ","pages":"Article 105459"},"PeriodicalIF":2.8,"publicationDate":"2025-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144748967","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}
Pub Date : 2025-07-20DOI: 10.1016/j.jnnfm.2025.105470
Austin Zapata , Andrea Vacca , Rich Diemar , Mark Hamersky , David Oertel
External gear machines are frequently used to transport non-Newtonian fluids in high pressure applications. However, a coexistence of low viscosity and significant shear thinning can present pumping challenges for off-the-shelf EGM designs. These difficulties arise in part due to the effects of viscoelasticity on the displacing action of the pump and the internal flow leakages. Previous studies have focused on three-dimensional CFD, but limited work has been done on a simulation tool for these effects which considers the radial micromotions of the gears. In this work, a fast lumped-parameter model for the simulation of external gear machines with non-Newtonian operating fluids is developed by dividing the pump into several control volumes and flow paths between them. A method of estimating flow for non-Newtonian fluid models is proposed as well as a novel Reynolds-type equation, and both are implemented within the model. The article then proceeds to compare the mean flow and pressure ripple predicted by this model with experiments to validate the methodology. The mean relative error of the model for the steady-state flowrate prediction is found to be 1.5 % and that of the amplitude prediction for the transient pressure ripple response is found to be 7.4 %. Finally, the results of the model are discussed and conclusions are drawn.
{"title":"A generalized lumped-parameter model for analyzing external gear machines with shear-thinning operating fluids","authors":"Austin Zapata , Andrea Vacca , Rich Diemar , Mark Hamersky , David Oertel","doi":"10.1016/j.jnnfm.2025.105470","DOIUrl":"10.1016/j.jnnfm.2025.105470","url":null,"abstract":"<div><div>External gear machines are frequently used to transport non-Newtonian fluids in high pressure applications. However, a coexistence of low viscosity and significant shear thinning can present pumping challenges for off-the-shelf EGM designs. These difficulties arise in part due to the effects of viscoelasticity on the displacing action of the pump and the internal flow leakages. Previous studies have focused on three-dimensional CFD, but limited work has been done on a simulation tool for these effects which considers the radial micromotions of the gears. In this work, a fast lumped-parameter model for the simulation of external gear machines with non-Newtonian operating fluids is developed by dividing the pump into several control volumes and flow paths between them. A method of estimating flow for non-Newtonian fluid models is proposed as well as a novel Reynolds-type equation, and both are implemented within the model. The article then proceeds to compare the mean flow and pressure ripple predicted by this model with experiments to validate the methodology. The mean relative error of the model for the steady-state flowrate prediction is found to be 1.5 % and that of the amplitude prediction for the transient pressure ripple response is found to be 7.4 %. Finally, the results of the model are discussed and conclusions are drawn.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"344 ","pages":"Article 105470"},"PeriodicalIF":2.7,"publicationDate":"2025-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144686338","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}
A comprehensive study was conducted on the dynamics of bubbles in a 0.10–0.40 wt% polyacrylamide (PAAM) solution in the presence and absence of a surfactant, considering various shape parameters and dimensionless numbers, for a broad range of bubble volumes, from 5 to 2000 mm3. A detailed rheological analysis is performed for the chemical solutions. A safe injection period is determined such that a bubble is unaffected by another one. Unsteady results are presented. Steadiness of the bubble is checked for various shape parameters, and safe column length is determined. Uncertainty analysis is also performed. Cusp formation at the bubble tail and its correlation with the surrounding stress were assessed using flow birefringence. No discontinuity in bubble velocity is reported. As the water-soluble surfactant, sodium dodecyl sulfate (SDS), is added at 10 and 100 ppm concentration, the bubbles stretch out more in the vertical direction, and cusp formation commences at a lower volume and is more pronounced.
{"title":"Dynamics of bubbles rising in viscoelastic liquids and birefringence measurement in the presence of a surfactant","authors":"Pınar Eribol , Arda Inanc , Ebru Sarioglu , Erkan Senses , A. Kerem Uguz","doi":"10.1016/j.jnnfm.2025.105458","DOIUrl":"10.1016/j.jnnfm.2025.105458","url":null,"abstract":"<div><div>A comprehensive study was conducted on the dynamics of bubbles in a 0.10–0.40 wt% polyacrylamide (PAAM) solution in the presence and absence of a surfactant, considering various shape parameters and dimensionless numbers, for a broad range of bubble volumes, from 5 to 2000 mm<sup>3</sup>. A detailed rheological analysis is performed for the chemical solutions. A safe injection period is determined such that a bubble is unaffected by another one. Unsteady results are presented. Steadiness of the bubble is checked for various shape parameters, and safe column length is determined. Uncertainty analysis is also performed. Cusp formation at the bubble tail and its correlation with the surrounding stress were assessed using flow birefringence. No discontinuity in bubble velocity is reported. As the water-soluble surfactant, sodium dodecyl sulfate (SDS), is added at 10 and 100 ppm concentration, the bubbles stretch out more in the vertical direction, and cusp formation commences at a lower volume and is more pronounced.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"344 ","pages":"Article 105458"},"PeriodicalIF":2.7,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144686182","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}
Pub Date : 2025-07-16DOI: 10.1016/j.jnnfm.2025.105467
Hamed Vaseghnia , Espen Jettestuen , Knut Erik Teigen Giljarhus , Olav Aursjø , Jan Ludvig Vinningland , Aksel Hiorth
In this study, we use a two-dimensional multiple relaxation time (MRT) approach for simulating polymeric fluids. A correction term is introduced into the source term to remove non-physical terms and improve numerical accuracy of the simulations. The correction term preserves the locality of the collision process and ensures numerical stability across a range of Weissenberg numbers when coupled with non-linear constitutive equations.
This approach is applied to the Phan-Thien-Tanner (PTT) model and the Oldroyd-B model, where the first exhibits viscoelastic and shear-thinning behavior while the second is purely viscoelastic. To evaluate the numerical accuracy and stability of the proposed MRT-LBM approach, we apply it to planar Poiseuille flow as well as simplified four-roll mill benchmarks. In the case of the four-roll mill, we specifically examine the effects of shear-thinning and viscoelasticity in steady elongational flows and their transitions to oscillatory and chaotic or turbulent behaviors, known as elastic instability. Our results indicate that the non-linearity in the stress-strain rate relationship and the microstructural dynamics of polymer chains, as described by non-linear constitutive models, make the standard BGK-LBM approach incapable to accurately capture the complex behavior of polymers without introducing numerical artifacts. On the other hand the MRT-LBM method maintains numerical stability and accuracy across a broad range of Weissenberg (up to ) and should therefore be the method of choice when simulating these types of flows.
{"title":"Enhanced double distribution function lattice Boltzmann method for simulation of viscoelastic and shear-thinning fluids flow","authors":"Hamed Vaseghnia , Espen Jettestuen , Knut Erik Teigen Giljarhus , Olav Aursjø , Jan Ludvig Vinningland , Aksel Hiorth","doi":"10.1016/j.jnnfm.2025.105467","DOIUrl":"10.1016/j.jnnfm.2025.105467","url":null,"abstract":"<div><div>In this study, we use a two-dimensional multiple relaxation time (MRT) approach for simulating polymeric fluids. A correction term is introduced into the source term to remove non-physical terms and improve numerical accuracy of the simulations. The correction term preserves the locality of the collision process and ensures numerical stability across a range of Weissenberg numbers when coupled with non-linear constitutive equations.</div><div>This approach is applied to the Phan-Thien-Tanner (PTT) model and the Oldroyd-B model, where the first exhibits viscoelastic and shear-thinning behavior while the second is purely viscoelastic. To evaluate the numerical accuracy and stability of the proposed MRT-LBM approach, we apply it to planar Poiseuille flow as well as simplified four-roll mill benchmarks. In the case of the four-roll mill, we specifically examine the effects of shear-thinning and viscoelasticity in steady elongational flows and their transitions to oscillatory and chaotic or turbulent behaviors, known as elastic instability. Our results indicate that the non-linearity in the stress-strain rate relationship and the microstructural dynamics of polymer chains, as described by non-linear constitutive models, make the standard BGK-LBM approach incapable to accurately capture the complex behavior of polymers without introducing numerical artifacts. On the other hand the MRT-LBM method maintains numerical stability and accuracy across a broad range of Weissenberg (up to <span><math><mrow><mi>W</mi><mi>i</mi><mo>=</mo><mn>20</mn></mrow></math></span>) and should therefore be the method of choice when simulating these types of flows.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"344 ","pages":"Article 105467"},"PeriodicalIF":2.7,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144678802","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}
Pub Date : 2025-07-10DOI: 10.1016/j.jnnfm.2025.105468
Oleg A. Logvinov , Isabel M. Irurzun
A renowned problem of a viscous fluid displacement by a less viscous one from a Hele-Shaw cell was considered. Both fluids exhibited viscoelastic Maxwell rheology with upper convective derivative. A unified approach, which is independent of particular rheology, was applied to derive averaged two-dimensional equations of motion (so-called Hele-Shaw models). The equations were based on Reynolds class averaging procedure. Linear stability analysis was performed under these new governing equations with a special set of boundary conditions for the case of viscoelastic fluids. Dispersion curves showed that, in contrast to the purely Newtonian case, two regimes of disturbance growth were possible: viscous and elastic. We studied the influence of the main dimensionless parameters, in particular, two Deborah numbers for a displacing and a displaced fluid, and the viscosity ratio, on the growth of small disturbances on the interface. In accordance with previous theoretical studies, in the elastic regime there is a disturbance with an infinite growth rate.
{"title":"Saffman – Taylor instability in poorly miscible viscoelastic flows","authors":"Oleg A. Logvinov , Isabel M. Irurzun","doi":"10.1016/j.jnnfm.2025.105468","DOIUrl":"10.1016/j.jnnfm.2025.105468","url":null,"abstract":"<div><div>A renowned problem of a viscous fluid displacement by a less viscous one from a Hele-Shaw cell was considered. Both fluids exhibited viscoelastic Maxwell rheology with upper convective derivative. A unified approach, which is independent of particular rheology, was applied to derive averaged two-dimensional equations of motion (so-called Hele-Shaw models). The equations were based on Reynolds class averaging procedure. Linear stability analysis was performed under these new governing equations with a special set of boundary conditions for the case of viscoelastic fluids. Dispersion curves showed that, in contrast to the purely Newtonian case, two regimes of disturbance growth were possible: viscous and elastic. We studied the influence of the main dimensionless parameters, in particular, two Deborah numbers for a displacing and a displaced fluid, and the viscosity ratio, on the growth of small disturbances on the interface. In accordance with previous theoretical studies, in the elastic regime there is a disturbance with an infinite growth rate.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"344 ","pages":"Article 105468"},"PeriodicalIF":2.7,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144653440","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}
Pub Date : 2025-07-09DOI: 10.1016/j.jnnfm.2025.105443
Ankush
The linear instability analysis of the isothermal pressure-driven flow of an Oldroyd-B fluid through a plane channel with viscous heating effects is carried out. The temperature dependence of the viscosity of solute, solvent, and polymeric solution is described using the Nahme law. There is no external temperature imposed in the system, the temperature gradient arises purely from frictional dissipation. The Reynolds number , Nahme number , Peclet number , Deborah number , the ratio of solvent to solution viscosity , and the dimensionless heating coefficient for polymeric solution are the dimensionless parameters that modify the instability characteristics of the flow. The Chebyshev spectral collocation method is employed to numerically solve the generalised eigenvalue problem. The viscous heating in the flow is characterised by Nahme number. It is observed that the unstable area under the neutral stability curves increases as we increase the viscous heating effects. Moreover, it is found that there exist a minimum and maximum threshold value of Deborah number for which linear instability persists. An increase in the value expands the parameter range for instability. The Peclet number and dimensionless heating coefficient do not alter the linear stability characteristics.
{"title":"Viscoelastic instability in viscosity-stratified channel flow with viscous heating effects","authors":"Ankush","doi":"10.1016/j.jnnfm.2025.105443","DOIUrl":"10.1016/j.jnnfm.2025.105443","url":null,"abstract":"<div><div>The linear instability analysis of the isothermal pressure-driven flow of an Oldroyd-B fluid through a plane channel with viscous heating effects is carried out. The temperature dependence of the viscosity of solute, solvent, and polymeric solution is described using the Nahme law. There is no external temperature imposed in the system, the temperature gradient arises purely from frictional dissipation. The Reynolds number <span><math><mrow><mo>(</mo><mi>R</mi><mi>e</mi><mo>)</mo></mrow></math></span>, Nahme number <span><math><mrow><mo>(</mo><mi>N</mi><mi>a</mi><mo>)</mo></mrow></math></span>, Peclet number <span><math><mrow><mo>(</mo><mi>P</mi><mi>e</mi><mo>)</mo></mrow></math></span>, Deborah number <span><math><mrow><mo>(</mo><mi>D</mi><mi>e</mi><mo>)</mo></mrow></math></span>, the ratio of solvent to solution viscosity <span><math><mrow><mo>(</mo><mi>β</mi><mo>)</mo></mrow></math></span>, and the dimensionless heating coefficient for polymeric solution <span><math><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow></math></span> are the dimensionless parameters that modify the instability characteristics of the flow. The Chebyshev spectral collocation method is employed to numerically solve the generalised eigenvalue problem. The viscous heating in the flow is characterised by Nahme number. It is observed that the unstable area under the neutral stability curves increases as we increase the viscous heating effects. Moreover, it is found that there exist a minimum and maximum threshold value of Deborah number for which linear instability persists. An increase in the <span><math><mi>β</mi></math></span> value expands the parameter range for instability. The Peclet number <span><math><mrow><mo>(</mo><mi>P</mi><mi>e</mi><mo>)</mo></mrow></math></span> and dimensionless heating coefficient <span><math><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow></math></span> do not alter the linear stability characteristics.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"344 ","pages":"Article 105443"},"PeriodicalIF":2.7,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144633530","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}
Pub Date : 2025-07-05DOI: 10.1016/j.jnnfm.2025.105455
P. Grassia , H. Rajabi , C. Torres-Ulloa , J. Hernández-Montelongo , J. Potter , J. Moston
A two-dimensional foam staircase structure is considered with bubbles stacked in a zigzag fashion along a channel. A model is analysed for determining the configuration of a staircase set into motion under the action of a high imposed driving pressure. Minimum and also maximum permitted bubble sizes for which the staircase structure survives are identified. Both minimum and maximum sizes are found to be decreasing functions of . Behaviours in the limit of large are identified, albeit tentatively, as the methodology for computing the staircase structure is found to be highly stiff. Indeed, as increases, tiny changes in the staircase configuration at the downstream end lead to large geometric changes at the upstream end, limiting the domain of values for which structures can be readily computed.
{"title":"A cluster of N-bubbles driven along a channel at high imposed driving pressure: Bubble areas, film lengths and vertex locations","authors":"P. Grassia , H. Rajabi , C. Torres-Ulloa , J. Hernández-Montelongo , J. Potter , J. Moston","doi":"10.1016/j.jnnfm.2025.105455","DOIUrl":"10.1016/j.jnnfm.2025.105455","url":null,"abstract":"<div><div>A two-dimensional foam staircase structure is considered with <span><math><mi>N</mi></math></span> bubbles stacked in a zigzag fashion along a channel. A model is analysed for determining the configuration of a staircase set into motion under the action of a high imposed driving pressure. Minimum and also maximum permitted bubble sizes for which the staircase structure survives are identified. Both minimum and maximum sizes are found to be decreasing functions of <span><math><mi>N</mi></math></span>. Behaviours in the limit of large <span><math><mi>N</mi></math></span> are identified, albeit tentatively, as the methodology for computing the staircase structure is found to be highly stiff. Indeed, as <span><math><mi>N</mi></math></span> increases, tiny changes in the staircase configuration at the downstream end lead to large geometric changes at the upstream end, limiting the domain of <span><math><mi>N</mi></math></span> values for which structures can be readily computed.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"344 ","pages":"Article 105455"},"PeriodicalIF":2.7,"publicationDate":"2025-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144580069","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}
Pub Date : 2025-06-24DOI: 10.1016/j.jnnfm.2025.105457
Noureddine Latrache , Fayçal Kelai , Yang Bai , Olivier Crumeyrolle , Innocent Mutabazi
Instabilities modes in viscoelastic Taylor-Couette flow are investigated using space-time diagrams and particle image velocimetry (PIV) of flow patterns in the meridional cross-section. The working solution is an aqueous mixture of the polymer solution of Polyethylene oxide (PEO) and Polyethylene glycol (PEG). The concentrations of the PEG and the POE are chosen in such a way to obtain solutions with constant shear viscosities (characteristic of Boger fluids) and a wide spectrum of values of the molecular elastic number in a single Taylor-Couette system. The interplay between the elasticity of the polymer solution and the inertia forces induced by the rotation of the cylinders leads to different critical modes: stationary Taylor vortices for very small values of the elasticity, ribbons i.e. superposition of spirals of opposite helicity for intermediate values of the elasticity and elastic vortices for large values of the elasticity and weak inertia forces. The elasto-rotational Rayleigh discriminant and linear stability analysis show the role of elasticity in the destabilization of the base flow and on the threshold of critical modes. The elastic vortices are characterized by regions of strong inflows separated by outflows; they form flame patterns in the spatiotemporal diagrams. The amplitude of the radial velocity at the centre of vortices is used as the order parameter of the ribbons dynamics. The Ginzburg-Landau theory offers a framework to describe the destabilization of regular ribbons with the introduction of a dissymmetry parameter. Spatiotemporal properties of elastic vortices (such as the drift velocity, the fraction, the size and the lifetime of inflows) are measured for different values of the criticality. The scaling exponents of energy spectra for inertio-elastic turbulence are determined for viscoelastic Taylor-Couette flow with the inner or outer sole rotating cylinder; the obtained values are compared with those from other experiments and from numerical simulations. PIV measurements have allowed to determine the power of the radial force at the inflow which shows that the driving mechanism of the elastic instability is active from the outer cylinder toward the inner cylinder.
{"title":"Quantitative characterization of the ribbons and elastic vortices in viscoelastic Taylor-Couette flow with Boger fluids","authors":"Noureddine Latrache , Fayçal Kelai , Yang Bai , Olivier Crumeyrolle , Innocent Mutabazi","doi":"10.1016/j.jnnfm.2025.105457","DOIUrl":"10.1016/j.jnnfm.2025.105457","url":null,"abstract":"<div><div>Instabilities modes in viscoelastic Taylor-Couette flow are investigated using space-time diagrams and particle image velocimetry (PIV) of flow patterns in the meridional cross-section. The working solution is an aqueous mixture of the polymer solution of Polyethylene oxide (PEO) and Polyethylene glycol (PEG). The concentrations of the PEG and the POE are chosen in such a way to obtain solutions with constant shear viscosities (characteristic of Boger fluids) and a wide spectrum of values of the molecular elastic number in a single Taylor-Couette system. The interplay between the elasticity of the polymer solution and the inertia forces induced by the rotation of the cylinders leads to different critical modes: stationary Taylor vortices for very small values of the elasticity, ribbons i.e. superposition of spirals of opposite helicity for intermediate values of the elasticity and elastic vortices for large values of the elasticity and weak inertia forces. The elasto-rotational Rayleigh discriminant and linear stability analysis show the role of elasticity in the destabilization of the base flow and on the threshold of critical modes. The elastic vortices are characterized by regions of strong inflows separated by outflows; they form flame patterns in the spatiotemporal diagrams. The amplitude of the radial velocity at the centre of vortices is used as the order parameter of the ribbons dynamics. The Ginzburg-Landau theory offers a framework to describe the destabilization of regular ribbons with the introduction of a dissymmetry parameter. Spatiotemporal properties of elastic vortices (such as the drift velocity, the fraction, the size and the lifetime of inflows) are measured for different values of the criticality. The scaling exponents of energy spectra for inertio-elastic turbulence are determined for viscoelastic Taylor-Couette flow with the inner or outer sole rotating cylinder; the obtained values are compared with those from other experiments and from numerical simulations. PIV measurements have allowed to determine the power of the radial force at the inflow which shows that the driving mechanism of the elastic instability is active from the outer cylinder toward the inner cylinder.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"343 ","pages":"Article 105457"},"PeriodicalIF":2.7,"publicationDate":"2025-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144522552","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}
Pub Date : 2025-06-22DOI: 10.1016/j.jnnfm.2025.105454
Haoqian Wang, Anik Tarafder, Kausik Sarkar
Pair interactions of viscous (constant viscosity) drops suspended in a shear-thinning viscous and viscoelastic shear flow are numerically investigated using a front-tracking method. Apart from the usual passing trajectories, where drops interact and slide past each other in the streamwise direction, we note two new trajectories. Shear-thinning (power law index n <1) introduces reversed trajectories, where after interaction the drops reverse directions, and viscoelasticity (nonzero Weissenberg number Wi) gives rise to tumbling trajectories, where the drops revolve around each other. In a viscous medium, only passing and reversed trajectories are seen in an n-Ca phase plot. Passing trajectories transition into reversed ones for small n (more shear-thinning) and low capillary numbers Ca with the critical n for transition increasing with decreasing capillary number. In a viscoelastic medium, one finds all three trajectories in an n-Wi phase plot: reversed trajectories for low Wi and low n, tumbling for high Wi and high n, and passing trajectories in between. The trajectories are explained in terms of the streamline topology around a single drop in shear: a region of reversed streamlines due to shear-thinning, and a region of spiraling streamlines due to viscoelasticity, both effects being more prominent for low Ca values (less deformable drops). Physical reasoning for the reversed streamlines in the presence of shear-thinning is offered, relating it to the pressure field.
{"title":"Pair interactions of viscous drops suspended in a shear-thinning viscous and viscoelastic shear flow","authors":"Haoqian Wang, Anik Tarafder, Kausik Sarkar","doi":"10.1016/j.jnnfm.2025.105454","DOIUrl":"10.1016/j.jnnfm.2025.105454","url":null,"abstract":"<div><div>Pair interactions of viscous (constant viscosity) drops suspended in a shear-thinning viscous and viscoelastic shear flow are numerically investigated using a front-tracking method. Apart from the usual passing trajectories, where drops interact and slide past each other in the streamwise direction, we note two new trajectories. Shear-thinning (power law index <em>n</em> <1) introduces reversed trajectories, where after interaction the drops reverse directions, and viscoelasticity (nonzero Weissenberg number <em>Wi</em>) gives rise to tumbling trajectories, where the drops revolve around each other. In a viscous medium, only passing and reversed trajectories are seen in an <em>n-Ca</em> phase plot. Passing trajectories transition into reversed ones for small <em>n</em> (more shear-thinning) and low capillary numbers <em>Ca</em> with the critical <em>n</em> for transition increasing with decreasing capillary number. In a viscoelastic medium, one finds all three trajectories in an <em>n-Wi</em> phase plot: reversed trajectories for low <em>Wi</em> and low <em>n</em>, tumbling for high <em>Wi</em> and high <em>n</em>, and passing trajectories in between. The trajectories are explained in terms of the streamline topology around a single drop in shear: a region of reversed streamlines due to shear-thinning, and a region of spiraling streamlines due to viscoelasticity, both effects being more prominent for low <em>Ca</em> values (less deformable drops). Physical reasoning for the reversed streamlines in the presence of shear-thinning is offered, relating it to the pressure field.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"344 ","pages":"Article 105454"},"PeriodicalIF":2.7,"publicationDate":"2025-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144534353","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}
Pub Date : 2025-06-21DOI: 10.1016/j.jnnfm.2025.105453
Giorgos Kanellopoulos
This study demonstrates that standing waves can arise in dry granular flows within a chute with mild sloped basal topography, even when the applied Froude number remains subcritical () and below the critical threshold for surface wave instability (). In the absence of basal topography, a stable uniform flow would be possible in this regime. By employing the Saint-Venant equations augmented with the rheology, we numerically observe the formation of these standing waves and confirm the negligible influence of the viscous diffusive term. A key finding is that these standing waves can be described by a single non-linear inviscid ordinary differential equation. While this equation lacks an analytical solution, we introduce a modified Euler’s method, a semi-analytical approach based on the equation’s direction field, to accurately capture the wave profile. For the special case of very gentle slopes, an implicit analytical approximation can be derived directly from the curve that corresponds to the zero inclination direction field (nullcline). Finally, we conduct numerical simulations using the full Saint-Venant equations to demonstrate that in the opposite Froude regime, when , even a very mild basal topography can induce the formation of roll waves and, furthermore, accelerate the coarsening process. It is shown that the generated roll waves can reach a steady state, even when the basal topography is present along the entire length of the chute. These results highlight the significant influence of topography on flow dynamics across different Froude number regimes.
{"title":"Formation of standing waves in granular chute flows induced by mild basal topography","authors":"Giorgos Kanellopoulos","doi":"10.1016/j.jnnfm.2025.105453","DOIUrl":"10.1016/j.jnnfm.2025.105453","url":null,"abstract":"<div><div>This study demonstrates that standing waves can arise in dry granular flows within a chute with mild sloped basal topography, even when the applied Froude number remains subcritical (<span><math><mrow><mi>F</mi><mi>r</mi><mo><</mo><mn>1</mn></mrow></math></span>) and below the critical threshold for surface wave instability (<span><math><mrow><mi>F</mi><mi>r</mi><mo><</mo><mi>F</mi><msub><mrow><mi>r</mi></mrow><mrow><mi>c</mi><mi>r</mi></mrow></msub></mrow></math></span>). In the absence of basal topography, a stable uniform flow would be possible in this regime. By employing the Saint-Venant equations augmented with the <span><math><mrow><mi>μ</mi><mrow><mo>(</mo><mi>I</mi><mo>)</mo></mrow></mrow></math></span> rheology, we numerically observe the formation of these standing waves and confirm the negligible influence of the viscous diffusive term. A key finding is that these standing waves can be described by a single non-linear inviscid ordinary differential equation. While this equation lacks an analytical solution, we introduce a modified Euler’s method, a semi-analytical approach based on the equation’s direction field, to accurately capture the wave profile. For the special case of very gentle slopes, an implicit analytical approximation can be derived directly from the curve that corresponds to the zero inclination direction field (nullcline). Finally, we conduct numerical simulations using the full Saint-Venant equations to demonstrate that in the opposite Froude regime, when <span><math><mrow><mi>F</mi><mi>r</mi><mo>></mo><mi>F</mi><msub><mrow><mi>r</mi></mrow><mrow><mi>c</mi><mi>r</mi></mrow></msub></mrow></math></span>, even a very mild basal topography can induce the formation of roll waves and, furthermore, accelerate the coarsening process. It is shown that the generated roll waves can reach a steady state, even when the basal topography is present along the entire length of the chute. These results highlight the significant influence of topography on flow dynamics across different Froude number regimes.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"343 ","pages":"Article 105453"},"PeriodicalIF":2.7,"publicationDate":"2025-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144522553","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}
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