Pub Date : 2025-02-18DOI: 10.1016/j.jnnfm.2025.105397
Jun Xu , Weicheng Yu , Chi Li , Likai Hou , Fubing Bao , Jie Li
Efficient mixing of chemicals is a key issue in microfluidics because of the limitations of low diffusivity in laminar flow. Induced charge electro-osmosis (ICEO), which generates quadrupole vortices, has been shown to be a simple and effective method for rapid mixing. The aim of this work is to improve the mixing of viscoelastic fluids using ICEO, thus extending the application of microfluidics in biomedical and chemical analysis. A simplified Phan–Thien–Tanner (sPTT) constitutive model was used to characterize the flow properties of the viscoelastic fluid, and the Navier-Stokes (NS) and Poisson-Nernst-Planck (PNP) equations were used to control the potential and ion concentration distributions, respectively. Numerical simulations of ICEO around a polarized cylinder in a two-dimensional cavity filled with an electrolyte solution have been carried out using the finite volume method. The effects of Weissenberg number (Wi), viscosity ratio (β), and extensibility parameter (ε) on the velocity and flow field were investigated. The results show that the larger ε and Wi are, the larger the maximum velocity is, and the peak velocity increases with increasing ε and Wi. When ε increases from 0.01 to 0.8, the peak velocity increases from 23.22 × 10−4 to 31.73 × 10−4. The maximum velocity at Wi = 10 is about twice that at Wi = 0.01.
{"title":"Influence of viscoelastic properties on induced charge electro-osmosis of Phan–Thien–Tanner fluids around a metal cylinder","authors":"Jun Xu , Weicheng Yu , Chi Li , Likai Hou , Fubing Bao , Jie Li","doi":"10.1016/j.jnnfm.2025.105397","DOIUrl":"10.1016/j.jnnfm.2025.105397","url":null,"abstract":"<div><div>Efficient mixing of chemicals is a key issue in microfluidics because of the limitations of low diffusivity in laminar flow. Induced charge electro-osmosis (ICEO), which generates quadrupole vortices, has been shown to be a simple and effective method for rapid mixing. The aim of this work is to improve the mixing of viscoelastic fluids using ICEO, thus extending the application of microfluidics in biomedical and chemical analysis. A simplified Phan–Thien–Tanner (sPTT) constitutive model was used to characterize the flow properties of the viscoelastic fluid, and the Navier-Stokes (NS) and Poisson-Nernst-Planck (PNP) equations were used to control the potential and ion concentration distributions, respectively. Numerical simulations of ICEO around a polarized cylinder in a two-dimensional cavity filled with an electrolyte solution have been carried out using the finite volume method. The effects of Weissenberg number (<em>Wi</em>), viscosity ratio (<em>β</em>), and extensibility parameter (<em>ε</em>) on the velocity and flow field were investigated. The results show that the larger <em>ε</em> and <em>Wi</em> are, the larger the maximum velocity is, and the peak velocity increases with increasing <em>ε</em> and <em>Wi</em>. When <em>ε</em> increases from 0.01 to 0.8, the peak velocity increases from 23.22 × 10<sup>−4</sup> to 31.73 × 10<sup>−4</sup>. The maximum velocity at <em>Wi</em> = 10 is about twice that at <em>Wi</em> = 0.01.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"337 ","pages":"Article 105397"},"PeriodicalIF":2.7,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143473956","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 : 2025-02-10DOI: 10.1016/j.jnnfm.2025.105396
Joe B. Joseph, Jonathan P. Rothstein
<div><div>Capillary breakup extensional rheometry (CaBER) is a technique widely used to quantitatively measure the transient extensional rheology of a visco-elastic fluid. In this paper, we investigate some of the shortcomings of measuring the transient relaxation time through CaBER and Dripping onto Substrate (DoS)-CaBER experimentation and describe problematic conditions for which consistency of results is not achieved. Using a high molecular weight polyacrylamide polymer <span><math><mrow><mo>(</mo><msub><mi>M</mi><mi>W</mi></msub><mo>=</mo><mn>18</mn><mi>x</mi><msup><mrow><mn>10</mn></mrow><mn>6</mn></msup><mrow><mi>g</mi><mo>/</mo><mtext>mol</mtext><mo>)</mo></mrow></mrow></math></span> in a viscous water and glycerol solution, we investigated the effect that the choice of syringe size, tubing size, tubing length and flow rate used to generate the liquid bridge in DoS-CaBER can have on the decay evolution of the fluid filament. The resulting measurements showed a sharp decrease in extensional viscosity and relaxation time with increasing strength of the shear and extensional flows within the syringe and tubing used to generate the pendant drop. These measurements highlighted the importance of considering the flow and deformation history of the polymer prior to the DoS-CaBER and CaBER stretches. In order to understand whether these observed effects were due to recoverable pre-deformation of the polymer or permanent scission of the polymer, the DoS-CaBER syringe setup was used to deposit the polymer solution into a CaBER under different loading conditions. CaBER tests were then performed with various delay times to erase the deformation history of loading. For these samples, rest times of more than 100 extensional relaxation times were required to erase the deformation history caused by the loading of the sample. Even with the pre-conditioning erased, however, unrecoverable losses in relaxation time and extensional viscosity remained. These observations indicate that polymer scission occurred in all samples where loading resulted in an extensional Weissenberg number greater than <span><math><mrow><mi>W</mi><mi>i</mi><mo>></mo><mn>8</mn><mrow></mrow><msup><mrow><mi>s</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span>. Next, the effect of successive CaBER stretches on a single sample and the time delay imposed between successive stretches on the fluid rheology was studied. Stretches performed immediately one after the other with no recovery time built in showed a steep decline in measured relaxation time and breakup time. However, even with post stretch delays of twenty minutes, full recovery of the initial fluid properties was not achieved suggesting that extensional flow induced scission of the polymer had occurred even in CaBER. Thus, it is clear that the effect of preconditioning a viscoelastic fluid is strong, and these factors need to be considered prior to conducting CaBER and DoS-CaBER experiments in the future.<
{"title":"Recovery dynamics and polymer scission in capillary breakup extensional rheometry","authors":"Joe B. Joseph, Jonathan P. Rothstein","doi":"10.1016/j.jnnfm.2025.105396","DOIUrl":"10.1016/j.jnnfm.2025.105396","url":null,"abstract":"<div><div>Capillary breakup extensional rheometry (CaBER) is a technique widely used to quantitatively measure the transient extensional rheology of a visco-elastic fluid. In this paper, we investigate some of the shortcomings of measuring the transient relaxation time through CaBER and Dripping onto Substrate (DoS)-CaBER experimentation and describe problematic conditions for which consistency of results is not achieved. Using a high molecular weight polyacrylamide polymer <span><math><mrow><mo>(</mo><msub><mi>M</mi><mi>W</mi></msub><mo>=</mo><mn>18</mn><mi>x</mi><msup><mrow><mn>10</mn></mrow><mn>6</mn></msup><mrow><mi>g</mi><mo>/</mo><mtext>mol</mtext><mo>)</mo></mrow></mrow></math></span> in a viscous water and glycerol solution, we investigated the effect that the choice of syringe size, tubing size, tubing length and flow rate used to generate the liquid bridge in DoS-CaBER can have on the decay evolution of the fluid filament. The resulting measurements showed a sharp decrease in extensional viscosity and relaxation time with increasing strength of the shear and extensional flows within the syringe and tubing used to generate the pendant drop. These measurements highlighted the importance of considering the flow and deformation history of the polymer prior to the DoS-CaBER and CaBER stretches. In order to understand whether these observed effects were due to recoverable pre-deformation of the polymer or permanent scission of the polymer, the DoS-CaBER syringe setup was used to deposit the polymer solution into a CaBER under different loading conditions. CaBER tests were then performed with various delay times to erase the deformation history of loading. For these samples, rest times of more than 100 extensional relaxation times were required to erase the deformation history caused by the loading of the sample. Even with the pre-conditioning erased, however, unrecoverable losses in relaxation time and extensional viscosity remained. These observations indicate that polymer scission occurred in all samples where loading resulted in an extensional Weissenberg number greater than <span><math><mrow><mi>W</mi><mi>i</mi><mo>></mo><mn>8</mn><mrow></mrow><msup><mrow><mi>s</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span>. Next, the effect of successive CaBER stretches on a single sample and the time delay imposed between successive stretches on the fluid rheology was studied. Stretches performed immediately one after the other with no recovery time built in showed a steep decline in measured relaxation time and breakup time. However, even with post stretch delays of twenty minutes, full recovery of the initial fluid properties was not achieved suggesting that extensional flow induced scission of the polymer had occurred even in CaBER. Thus, it is clear that the effect of preconditioning a viscoelastic fluid is strong, and these factors need to be considered prior to conducting CaBER and DoS-CaBER experiments in the future.<","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"337 ","pages":"Article 105396"},"PeriodicalIF":2.7,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143427714","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 : 2025-02-07DOI: 10.1016/j.jnnfm.2025.105393
C. Sasmal
Viscoelastic fluids, a subclass of complex fluids, are employed across various applications, from biological processes to large-scale industrial operations. These fluids exhibit complex flow behaviors resulting from non-linear elastic stresses that arise from the stretching and relaxation of their microstructures, such as polymer molecules in viscoelastic polymer solutions, within a deformed flow field. One notable phenomenon associated with these fluids is purely “elastic instability” (EI), which occurs when elastic stresses interact with the streamline curvature in a flow system at low Reynolds numbers (the ratio of inertial to viscous forces). Specifically, EI manifests when the Weissenberg number (the ratio of the microstructure relaxation time to the rate of flow deformation) surpasses a critical threshold. As the Weissenberg number continues to increase, the unstable flow field resulting from EI further transits to a more chaotic and turbulent-like flow state known as “elastic turbulence” (ET). The fluctuating hydrodynamics characteristics of ET display statistical similarities to conventional Newtonian turbulence observed at high Reynolds numbers. Over the past two decades or so, extensive research has been conducted within the complex fluids research community to explore these two phenomena, resulting in several comprehensive articles that outline the development and understanding of ET. This article focuses on the potential application perspectives of these two phenomena. In particular, this article aims to provide a thorough review of the applications of EI and ET phenomena, particularly in three main areas: microfluidic mixing, microscale heat transfer, and chemically enhanced oil recovery (EOR) processes. Furthermore, this review will also provide a discussion on the limitations and future research directions associated with these two phenomena, highlighting their potential from an application standpoint.
{"title":"Potential applications of elastic instability and elastic turbulence: A comprehensive review, limitations, and future directions","authors":"C. Sasmal","doi":"10.1016/j.jnnfm.2025.105393","DOIUrl":"10.1016/j.jnnfm.2025.105393","url":null,"abstract":"<div><div>Viscoelastic fluids, a subclass of complex fluids, are employed across various applications, from biological processes to large-scale industrial operations. These fluids exhibit complex flow behaviors resulting from non-linear elastic stresses that arise from the stretching and relaxation of their microstructures, such as polymer molecules in viscoelastic polymer solutions, within a deformed flow field. One notable phenomenon associated with these fluids is purely “elastic instability” (EI), which occurs when elastic stresses interact with the streamline curvature in a flow system at low Reynolds numbers (the ratio of inertial to viscous forces). Specifically, EI manifests when the Weissenberg number (the ratio of the microstructure relaxation time to the rate of flow deformation) surpasses a critical threshold. As the Weissenberg number continues to increase, the unstable flow field resulting from EI further transits to a more chaotic and turbulent-like flow state known as “elastic turbulence” (ET). The fluctuating hydrodynamics characteristics of ET display statistical similarities to conventional Newtonian turbulence observed at high Reynolds numbers. Over the past two decades or so, extensive research has been conducted within the complex fluids research community to explore these two phenomena, resulting in several comprehensive articles that outline the development and understanding of ET. This article focuses on the potential application perspectives of these two phenomena. In particular, this article aims to provide a thorough review of the applications of EI and ET phenomena, particularly in three main areas: microfluidic mixing, microscale heat transfer, and chemically enhanced oil recovery (EOR) processes. Furthermore, this review will also provide a discussion on the limitations and future research directions associated with these two phenomena, highlighting their potential from an application standpoint.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"337 ","pages":"Article 105393"},"PeriodicalIF":2.7,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419591","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 : 2025-02-01DOI: 10.1016/j.jnnfm.2024.105381
Hala Krir, Abdelhak Ayadi
The present paper aims to investigate the phenomenon of extrudate swells of polydimethylsiloxane (PDMS) during extrusion. This study contributes to understanding how radial flow, and in particular gap width, influences the initiation and growth of linear PDMS extruded swelling. To accomplish this, we consider implementing a capillary rheometer that imposes a radial flow upstream of the extrusion die. Images from the experiment demonstrate that the die swell seems more pronounced for both long and short dies with a high radial flow gap than it does for small gaps. In addition, we notice that, for a given gap, an increase in the length-to-diameter ratio reduces the extrudate swell. The findings explore the interplay between the elasticity of PDMS, the energy stored during the flow, and the memory effect on the final diameter of the extruded material.
{"title":"Extrudate swell and defects under the effect of radial flow and die geometry","authors":"Hala Krir, Abdelhak Ayadi","doi":"10.1016/j.jnnfm.2024.105381","DOIUrl":"10.1016/j.jnnfm.2024.105381","url":null,"abstract":"<div><div>The present paper aims to investigate the phenomenon of extrudate swells of polydimethylsiloxane (PDMS) during extrusion. This study contributes to understanding how radial flow, and in particular gap width, influences the initiation and growth of linear PDMS extruded swelling. To accomplish this, we consider implementing a capillary rheometer that imposes a radial flow upstream of the extrusion die. Images from the experiment demonstrate that the die swell seems more pronounced for both long and short dies with a high radial flow gap than it does for small gaps. In addition, we notice that, for a given gap, an increase in the length-to-diameter ratio reduces the extrudate swell. The findings explore the interplay between the elasticity of PDMS, the energy stored during the flow, and the memory effect on the final diameter of the extruded material.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"336 ","pages":"Article 105381"},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143153122","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 : 2025-02-01DOI: 10.1016/j.jnnfm.2024.105379
L. Talon, D. Salin
Recent experiments on pressure-driven Poiseuille flow of cornstarch in a cylindrical tube (Talon and Salin, 2024) show a surprising behavior. The measured flow curve, i.e. the flow rate versus the applied pressure drop, is indeed non-monotonic: the flow rate increases monotonically at low pressure drops up to a maximum, after which it decreases abruptly to an almost constant flow rate regardless of further increases in pressure drop. Cornstarch is known to exhibit discontinuous shear thickening (DST) behavior (Fall et al., 2012). In addition, recent experiments (Denn et al., 2018; Darbois Texier et al., 2020; Bougouin et al., 2024) suggest that the rheology may ultimately be S-shaped, where the shear rate is a nonmonotonic function of stress, similar to the model proposed by Wyart and Cates (Wyart and Cates, 2014). To account for the observed jump-plateau behavior of the flow rate, one possibility is that Poiseuille flow for S-shaped rheology exhibits some kind of phase segregation, where the pressure gradient becomes non-uniform. The pressure gradient segregate between two types of region, with either high pressure gradient or low one. This kind of “streamwise banding” were analyzed in Talon and Salin (2024) using the lubrication approximation and assuming simple dynamical stochastic version of the nonmonotonic S-shaped rheology Wyart–Cates model. The plateau behavior is then related to an increase of the high viscous region as the pressure is increased. The mere presence of a non-monotonic rheological curve could then be sufficient to predict the occurrence of banding in the streamwise direction, even if the suspension remains homogeneous.
In this paper, we aim to analyze this prediction by disregarding the lubrication approximation and directly solving the flow of a shear thickening fluid with S-shaped rheology. Using 2D TRT Lattice Boltzmann simulations, we observe that the plateau in flow rate is indeed associated with a streamwise segregation of the pressure gradient. In addition, we show that regions of high pressure gradients are due to the formation of a highly viscous structure similar to a “sandglass” shape. We then analyze the occurrence of these sandglass structures as a function of the system parameters.
{"title":"Numerical simulation of Poiseuille flow for S-shaped rheology fluid: Streamwise banding and viscous sandglasses","authors":"L. Talon, D. Salin","doi":"10.1016/j.jnnfm.2024.105379","DOIUrl":"10.1016/j.jnnfm.2024.105379","url":null,"abstract":"<div><div>Recent experiments on pressure-driven Poiseuille flow of cornstarch in a cylindrical tube (Talon and Salin, 2024) show a surprising behavior. The measured flow curve, i.e. the flow rate versus the applied pressure drop, is indeed non-monotonic: the flow rate increases monotonically at low pressure drops up to a maximum, after which it decreases abruptly to an almost constant flow rate regardless of further increases in pressure drop. Cornstarch is known to exhibit discontinuous shear thickening (DST) behavior (Fall et al., 2012). In addition, recent experiments (Denn et al., 2018; Darbois Texier et al., 2020; Bougouin et al., 2024) suggest that the rheology may ultimately be S-shaped, where the shear rate is a nonmonotonic function of stress, similar to the model proposed by Wyart and Cates (Wyart and Cates, 2014). To account for the observed jump-plateau behavior of the flow rate, one possibility is that Poiseuille flow for S-shaped rheology exhibits some kind of phase segregation, where the pressure gradient becomes non-uniform. The pressure gradient segregate between two types of region, with either high pressure gradient or low one. This kind of “streamwise banding” were analyzed in Talon and Salin (2024) using the lubrication approximation and assuming simple dynamical stochastic version of the nonmonotonic S-shaped rheology Wyart–Cates model. The plateau behavior is then related to an increase of the high viscous region as the pressure is increased. The mere presence of a non-monotonic rheological curve could then be sufficient to predict the occurrence of banding in the streamwise direction, even if the suspension remains homogeneous.</div><div>In this paper, we aim to analyze this prediction by disregarding the lubrication approximation and directly solving the flow of a shear thickening fluid with S-shaped rheology. Using 2D TRT Lattice Boltzmann simulations, we observe that the plateau in flow rate is indeed associated with a streamwise segregation of the pressure gradient. In addition, we show that regions of high pressure gradients are due to the formation of a highly viscous structure similar to a “sandglass” shape. We then analyze the occurrence of these sandglass structures as a function of the system parameters.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"336 ","pages":"Article 105379"},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143154453","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 : 2025-02-01DOI: 10.1016/j.jnnfm.2025.105384
Milad Mousavi, Yannis Dimakopoulos, John Tsamopoulos
We examine computationally the two-dimensional flow of elastoviscoplastic (EVP) fluids around a cylinder symmetrically placed between two plates parallel to its axis. The Saramito-Herschel-Bulkley fluid model is solved via the finite-volume method using the OpenFOAM software. As in viscoplastic materials, unyielded regions arise around the plane of symmetry well ahead or behind the cylinder, as two small islands located above and below the cylinder and as polar caps at the two stagnation points on the cylinder. Most interestingly, under certain conditions, an elongated yielded area around the midplane is predicted downstream of the cylinder, sandwiched between two unyielded areas. This surprising result appears, for example, with Carbopol 0.1 % when considering a blockage ratio of 0.5 (the ratio of the cylinder's diameter to the channel's width) and above a critical elastic modulus (). An approximate semi-analytical solution using the same model, in the region mentioned above reveals that it is caused by the intense variation of the stress magnitude there, which may approach the yield stress asymptotically either from above or below, depending on material elasticity. The drag coefficient on the cylinder increases with yield stress and blockage ratio but decreases with material elasticity. The unyielded regions expand as the yield stress increases. They also expand when material elasticity increases because this allows the material to elastically deform more before yielding. Behind the cylinder, the so-called "negative wake" appears which becomes more intense as elasticity increases. Furthermore, by decreasing the elastic modulus or increasing the yield stress beyond a critical value, the yield surface may exhibit damped oscillations, or irregular shapes even without a plane of symmetry, all under creeping flow conditions. Both properties generate these patterns mainly behind the cylinder, because they increase the elastic stresses and the curvature of the streamlines triggering a purely elastic instability.
{"title":"Elasto-visco-plastic flows in benchmark geometries: II. Flow around a confined cylinder","authors":"Milad Mousavi, Yannis Dimakopoulos, John Tsamopoulos","doi":"10.1016/j.jnnfm.2025.105384","DOIUrl":"10.1016/j.jnnfm.2025.105384","url":null,"abstract":"<div><div>We examine computationally the two-dimensional flow of elastoviscoplastic (EVP) fluids around a cylinder symmetrically placed between two plates parallel to its axis. The Saramito-Herschel-Bulkley fluid model is solved via the finite-volume method using the OpenFOAM software. As in viscoplastic materials, unyielded regions arise around the plane of symmetry well ahead or behind the cylinder, as two small islands located above and below the cylinder and as polar caps at the two stagnation points on the cylinder. Most interestingly, under certain conditions, an elongated yielded area around the midplane is predicted downstream of the cylinder, sandwiched between two unyielded areas. This surprising result appears, for example, with Carbopol 0.1 % when considering a blockage ratio of 0.5 (the ratio of the cylinder's diameter to the channel's width) and above a critical elastic modulus (<span><math><mrow><mi>G</mi><mo>></mo><mn>30</mn><mspace></mspace><mi>P</mi><mi>a</mi></mrow></math></span>). An approximate semi-analytical solution using the same model, in the region mentioned above reveals that it is caused by the intense variation of the stress magnitude there, which may approach the yield stress asymptotically either from above or below, depending on material elasticity. The drag coefficient on the cylinder increases with yield stress and blockage ratio but decreases with material elasticity. The unyielded regions expand as the yield stress increases. They also expand when material elasticity increases because this allows the material to elastically deform more before yielding. Behind the cylinder, the so-called \"negative wake\" appears which becomes more intense as elasticity increases. Furthermore, by decreasing the elastic modulus or increasing the yield stress beyond a critical value, the yield surface may exhibit damped oscillations, or irregular shapes even without a plane of symmetry, all under creeping flow conditions. Both properties generate these patterns mainly behind the cylinder, because they increase the elastic stresses and the curvature of the streamlines triggering a purely elastic instability.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"336 ","pages":"Article 105384"},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143153123","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 : 2025-02-01DOI: 10.1016/j.jnnfm.2024.105366
P. Moschopoulos, Y. Dimakopoulos, J. Tsamopoulos
When the accurate simulation of two materials that interact through their common and deformable interface is of interest, the efficient treatment of the interface determines the success or failure of a numerical method. In this work, we propose a new, robust and easy-to-code finite element formulation for such interaction problems. The remedy of the interface constraints, namely the continuity of velocities and stresses, is accomplished using a single-node approach and the same continuous basis functions for the velocities in both materials. Given that only Newtonian fluids will be examined, we do not have to introduce basis functions for the stress components. The XFEM method, which enriches locally the continuous basis function of a variable that presents a discontinuity, is employed to tackle the discontinuous behavior of the pressure across the interface. The incorporation of Petrov-Galerkin stabilization schemes enhances further our formulation and allows the usage of equal order interpolants for velocities and pressure. We solve the coupled system of equations in a monolithic manner to alleviate the convergence problems of the segregated approach. The novel aspect of our method is that its ingredients do not differentiate based on the constituent materials of the problem, and it can be used interchangeably for either a fluid-structure or a fluid-fluid interaction problem. The accuracy of the new finite element formulation is assessed by comparing its numerical results to those of the literature in three problems: i) the flow through a partially collapsible channel, ii) the induced motion of a flexible elastic plate, iii) the filament stretching of a Newtonian thread surrounded by another immiscible viscous fluid. In all cases, we are in agreement with the results of the literature. Furthermore, we conduct a challenging, 3D simulation for a setup that resembles the motion of a three-leaflet stented aortic heart valve.
{"title":"A new finite element formulation unifying fluid-structure and fluid-fluid interaction problems","authors":"P. Moschopoulos, Y. Dimakopoulos, J. Tsamopoulos","doi":"10.1016/j.jnnfm.2024.105366","DOIUrl":"10.1016/j.jnnfm.2024.105366","url":null,"abstract":"<div><div>When the accurate simulation of two materials that interact through their common and deformable interface is of interest, the efficient treatment of the interface determines the success or failure of a numerical method. In this work, we propose a new, robust and easy-to-code finite element formulation for such interaction problems. The remedy of the interface constraints, namely the continuity of velocities and stresses, is accomplished using a single-node approach and the same continuous basis functions for the velocities in both materials. Given that only Newtonian fluids will be examined, we do not have to introduce basis functions for the stress components. The XFEM method, which enriches locally the continuous basis function of a variable that presents a discontinuity, is employed to tackle the discontinuous behavior of the pressure across the interface. The incorporation of Petrov-Galerkin stabilization schemes enhances further our formulation and allows the usage of equal order interpolants for velocities and pressure. We solve the coupled system of equations in a monolithic manner to alleviate the convergence problems of the segregated approach. The novel aspect of our method is that its ingredients do not differentiate based on the constituent materials of the problem, and it can be used interchangeably for either a fluid-structure or a fluid-fluid interaction problem. The accuracy of the new finite element formulation is assessed by comparing its numerical results to those of the literature in three problems: i) the flow through a partially collapsible channel, ii) the induced motion of a flexible elastic plate, iii) the filament stretching of a Newtonian thread surrounded by another immiscible viscous fluid. In all cases, we are in agreement with the results of the literature. Furthermore, we conduct a challenging, 3D simulation for a setup that resembles the motion of a three-leaflet stented aortic heart valve.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"336 ","pages":"Article 105366"},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143153120","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 : 2025-02-01DOI: 10.1016/j.jnnfm.2024.105376
Kindness Isukwem, Anselmo Pereira
In this note, we numerically and theoretically analyze the physical mechanisms controlling the gravity-induced spreading of viscoplastic elliptical metric objects on a sticky solid surface (without sliding). The two-dimensional collapsing objects are described as Bingham fluids. The numerical simulations are based on a variational multi-scale approach devoted to multiphase non-Newtonian fluid flows. The results are depicted by considering the spreading dynamics, energy budgets, and new scaling laws. They show that, under negligible inertial effects, the driving gravitational energy of the elliptical columns is dissipated through viscoplastic effects during the collapse, giving rise to three flow regimes: gravito-viscous, gravito-plastic, and mixed gravito-visco-plastic. These regimes are strongly affected by the initial aspect ratio of the collapsing column, which reveals the possibility of using morphology to control spreading. Finally, the results are summarized in a diagram linking the object’s maximum spreading and the collapse time with different collapsing regimes through a single dimensionless parameter called collapse number.
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The viscoelastic flow of a surfactant solution in a continuous contraction-expansion flow channel exhibits three types of characteristic flows based on Reynolds numbers. At low Reynolds numbers, the Barus effect is observed in a cavity of the channel. At high Reynolds number, the separation flow, where the main flow separates from the fluids in the cavity, is observed, and the flow does not penetrate the cavity. At moderate Reynolds numbers, the fluid penetrates the cavity at the cavity midsection, changes the flow direction to the opposite direction of the main flow, returns to the forward direction near the upstream wall of the cavity, and flows out of the cavity. The flow regime is called the bulge structure. The bulge structure is an interesting flow regime observed in the cavity only when the surfactant solution exhibits high viscoelasticity. Three-dimensional velocity fields in the cavity were measured using particle tracking velocimetry (PTV) to elucidate the mechanism of the bulge structure appearance. From the three-dimensional velocity measurements, the unique velocity fields of the bulge structure were obtained. In particular, the spanwise velocity of the bulge structure was much higher at the cavity inlet and outlet than that at the Barus effect. This indicates that the expansion and contraction flow in the spanwise direction result in the bulge structure. A high spanwise flow was observed at the cavity inlet and outlet, which may have resulted from the expansion flow. Thus, the expansion flow, not only in the flow direction but also in the spanwise direction, generates the bulge structure in the cavity. In this study, the formation mechanism of the bulge structure was elucidated.
{"title":"Three-dimensional velocity fields measurement of bulge structure observed in a cavity via particle tracking velocimetry","authors":"Hideki Sato , Masaki Kawata , Ruri Hidema , Hiroshi Suzuki","doi":"10.1016/j.jnnfm.2025.105383","DOIUrl":"10.1016/j.jnnfm.2025.105383","url":null,"abstract":"<div><div>The viscoelastic flow of a surfactant solution in a continuous contraction-expansion flow channel exhibits three types of characteristic flows based on Reynolds numbers. At low Reynolds numbers, the Barus effect is observed in a cavity of the channel. At high Reynolds number, the separation flow, where the main flow separates from the fluids in the cavity, is observed, and the flow does not penetrate the cavity. At moderate Reynolds numbers, the fluid penetrates the cavity at the cavity midsection, changes the flow direction to the opposite direction of the main flow, returns to the forward direction near the upstream wall of the cavity, and flows out of the cavity. The flow regime is called the bulge structure. The bulge structure is an interesting flow regime observed in the cavity only when the surfactant solution exhibits high viscoelasticity. Three-dimensional velocity fields in the cavity were measured using particle tracking velocimetry (PTV) to elucidate the mechanism of the bulge structure appearance. From the three-dimensional velocity measurements, the unique velocity fields of the bulge structure were obtained. In particular, the spanwise velocity of the bulge structure was much higher at the cavity inlet and outlet than that at the Barus effect. This indicates that the expansion and contraction flow in the spanwise direction result in the bulge structure. A high spanwise flow was observed at the cavity inlet and outlet, which may have resulted from the expansion flow. Thus, the expansion flow, not only in the flow direction but also in the spanwise direction, generates the bulge structure in the cavity. In this study, the formation mechanism of the bulge structure was elucidated.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"336 ","pages":"Article 105383"},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143154449","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 : 2025-02-01DOI: 10.1016/j.jnnfm.2024.105377
Xiaoyang Xu , Lingyun Tian , Yijie Sun , Jiangnan Kang
In the present work, we introduce a smoothed particle hydrodynamics (SPH) method for simulating both 2D and 3D transient non-isothermal viscoelastic injection molding process with complex-shaped cavities. To delineate the viscoelastic properties of the polymer melt, the non-isothermal Oldroyd-B constitutive equation is considered based on the time–temperature superposition principle. To discretize the governing equations, the improved SPH scheme presented by Xu and Jiang, J. Non-Newtonian Fluid Mech. 309 (2022) pp. 104,905 is employed. To model the wall boundaries of complex shapes, an enhanced treatment technique of wall boundaries that utilizes a level-set based pre-processing algorithm is introduced. Initially, the method is applied to simulate a 2D non-isothermal viscoelastic injection molding process involving a circular disc with an irregular insert. The convergence of the method is validated by three different particle sizes. Results on the velocity, temperature, and the first normal stress difference during the injection molding process are presented. The influences of the Péclet, Reynolds, Weissenberg numbers, and viscosity ratio on the process are analyzed. The method is then extended to handle challenging 3D non-isothermal viscoelastic injection molding problems, including cavities of a hexagon screw and a car rim. Change in rheological information at various time points is reported. All the results demonstrate that the proposed SPH method is a robust computation tool for simulations of both 2D and 3D transient non-isothermal viscoelastic injection molding processes, even with highly complex-shaped cavities.
{"title":"2D and 3D SPH simulations of transient non-isothermal viscoelastic injection molding process with complex-shaped cavities","authors":"Xiaoyang Xu , Lingyun Tian , Yijie Sun , Jiangnan Kang","doi":"10.1016/j.jnnfm.2024.105377","DOIUrl":"10.1016/j.jnnfm.2024.105377","url":null,"abstract":"<div><div>In the present work, we introduce a smoothed particle hydrodynamics (SPH) method for simulating both 2D and 3D transient non-isothermal viscoelastic injection molding process with complex-shaped cavities. To delineate the viscoelastic properties of the polymer melt, the non-isothermal Oldroyd-B constitutive equation is considered based on the time–temperature superposition principle. To discretize the governing equations, the improved SPH scheme presented by Xu and Jiang, J. Non-Newtonian Fluid Mech. 309 (2022) pp. 104,905 is employed. To model the wall boundaries of complex shapes, an enhanced treatment technique of wall boundaries that utilizes a level-set based pre-processing algorithm is introduced. Initially, the method is applied to simulate a 2D non-isothermal viscoelastic injection molding process involving a circular disc with an irregular insert. The convergence of the method is validated by three different particle sizes. Results on the velocity, temperature, and the first normal stress difference during the injection molding process are presented. The influences of the Péclet, Reynolds, Weissenberg numbers, and viscosity ratio on the process are analyzed. The method is then extended to handle challenging 3D non-isothermal viscoelastic injection molding problems, including cavities of a hexagon screw and a car rim. Change in rheological information at various time points is reported. All the results demonstrate that the proposed SPH method is a robust computation tool for simulations of both 2D and 3D transient non-isothermal viscoelastic injection molding processes, even with highly complex-shaped cavities.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"336 ","pages":"Article 105377"},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143153118","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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