Pub Date : 2025-03-01Epub 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":"2025-03-01","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 : 2025-02-01Epub Date: 2024-12-19DOI: 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.
最近关于玉米淀粉在圆柱形管中压力驱动的泊泽维尔流动的实验（Talon和Salin， 2024）显示了令人惊讶的行为。测量到的流量曲线，即流量与施加压降的关系，确实是非单调的：在低压下，流量单调增加，直到达到最大值，然后，无论压降进一步增加，流量都突然下降到几乎恒定的流量。已知玉米淀粉具有不连续剪切增稠（DST）行为（Fall et al., 2012）。此外，最近的实验(Denn et al., 2018；Darbois Texier et al., 2020；Bougouin et al., 2024)认为流变最终可能是s形的，剪切速率是应力的非单调函数，类似于Wyart and Cates提出的模型（Wyart and Cates, 2014）。为了解释所观察到的流量跳台行为，一种可能性是s形流变的泊泽维尔流表现出某种相分离，其中压力梯度变得不均匀。压力梯度在高压力梯度和低压力梯度两种类型的区域之间分离。Talon和Salin（2024）使用润滑近似并假设非单调s形流变wyart - gates模型的简单动态随机版本分析了这种“流向带状”。当压力增加时，平台特性与高粘性区域的增加有关。即使悬浮液保持均匀，非单调流变曲线的存在也足以预测沿流方向出现带状。在本文中，我们的目的是通过不考虑润滑近似，直接求解具有s型流变的剪切增稠流体的流动来分析这一预测。利用二维TRT晶格玻尔兹曼模拟，我们观察到流量的平台确实与压力梯度的顺流分离有关。此外，我们还表明，高压梯度区域是由于形成了类似于“沙漏”形状的高粘性结构。然后，我们分析了这些沙漏结构作为系统参数的函数。
{"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 : 2025-02-01Epub Date: 2024-12-19DOI: 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 : 2025-02-01Epub Date: 2025-01-14DOI: 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 : 2025-02-01Epub Date: 2024-12-02DOI: 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}
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 : 2025-02-01Epub Date: 2024-12-19DOI: 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.
{"title":"Dam break of viscoplastic elliptical objects","authors":"Kindness Isukwem, Anselmo Pereira","doi":"10.1016/j.jnnfm.2024.105376","DOIUrl":"10.1016/j.jnnfm.2024.105376","url":null,"abstract":"<div><div>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 <em>collapse number</em>.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"336 ","pages":"Article 105376"},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143153779","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 : 2025-02-01Epub Date: 2024-12-09DOI: 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}
Pub Date : 2025-02-01Epub Date: 2024-12-12DOI: 10.1016/j.jnnfm.2024.105378
Nan-Yang Zhao , Bin Xue , Ming-Yang Su , Zhong-Bin Xu , Qiong Wu , Jing Zhou
<div><div>The thorough analysis of thermal effects in the interior of molds enhances the understanding of the role and evolution of flow-thermal interactions during injection molding. However, current methods that incorporate heating and insulation devices for detecting melt within molds do not accurately reflect actual manufacturing environments. The non-isothermal conditions in molds also complicate the quantitative analysis of thermal effects, posing challenges for in-mold analysis. In this study, we proposed a comprehensive analytical and validation approach to investigate the significance of viscous dissipation in a non-adiabatic mold during injection molding. Channel dimensions (fixed length of 25 mm, radii of 0.75–1.5 mm) and melt velocities (25–150 mm s<sup>−1</sup>) were adjusted to observe pressure drop variations (<span><math><mrow><mstyle><mi>Δ</mi></mstyle><msub><mi>P</mi><mtext>en</mtext></msub></mrow></math></span>) in a special-designed mold. An equivalent pressure concept (<span><math><mrow><mstyle><mi>Δ</mi></mstyle><msub><mi>P</mi><mtext>vis</mtext></msub></mrow></math></span>) was proposed to assess temperature variations induced by viscous dissipation. Dimensionless indices related to channel dimensions (<span><math><msub><mi>I</mi><mrow><mi>P</mi><mo>_</mo><mi>R</mi></mrow></msub></math></span> and <span><math><msub><mi>I</mi><mrow><mtext>Pcor</mtext><mo>_</mo><mi>R</mi></mrow></msub></math></span>) and melt injection velocities (<span><math><msub><mi>I</mi><mrow><mi>P</mi><mo>_</mo><mi>v</mi></mrow></msub></math></span> and <span><math><msub><mi>I</mi><mrow><mtext>Pcor</mtext><mo>_</mo><mi>v</mi></mrow></msub></math></span>) were established to observe pressure drop (<span><math><mrow><mstyle><mi>Δ</mi></mstyle><msub><mi>P</mi><mtext>en</mtext></msub></mrow></math></span>) and corrected pressure drop (<span><math><mrow><mstyle><mi>Δ</mi></mstyle><msub><mi>P</mi><mtext>cor</mtext></msub></mrow></math></span>). The results indicate that the corrected pressure drop and viscosity curves (<span><math><mrow><mstyle><mi>Δ</mi></mstyle><msub><mi>P</mi><mtext>cor</mtext></msub></mrow></math></span> and <span><math><msub><mi>η</mi><mtext>cor</mtext></msub></math></span>) show more consistent variations versus channel dimensions and melt velocities when the viscous dissipation effect is quantitatively incorporated into melt pressure and viscosity analyses (<span><math><mrow><mstyle><mi>Δ</mi></mstyle><msub><mi>P</mi><mtext>en</mtext></msub></mrow></math></span> and <span><math><mi>η</mi></math></span>), aligning closely with observations under adiabatic conditions. Thermal-related dimensionless numbers (Eckert, Brinkman, and Peclet numbers) qualitatively confirm the significance of viscous dissipation. This study offers a comprehensive analysis and validation of thermal effects in mold, presenting a novel method for exploring specific melt behaviors and advancing the analysis of mold interiors in non-adiabatic environments.</div></div
{"title":"Significance of viscous dissipation effect during the rapid filling process in the non-adiabatic mold: A full analytical and validating solution","authors":"Nan-Yang Zhao , Bin Xue , Ming-Yang Su , Zhong-Bin Xu , Qiong Wu , Jing Zhou","doi":"10.1016/j.jnnfm.2024.105378","DOIUrl":"10.1016/j.jnnfm.2024.105378","url":null,"abstract":"<div><div>The thorough analysis of thermal effects in the interior of molds enhances the understanding of the role and evolution of flow-thermal interactions during injection molding. However, current methods that incorporate heating and insulation devices for detecting melt within molds do not accurately reflect actual manufacturing environments. The non-isothermal conditions in molds also complicate the quantitative analysis of thermal effects, posing challenges for in-mold analysis. In this study, we proposed a comprehensive analytical and validation approach to investigate the significance of viscous dissipation in a non-adiabatic mold during injection molding. Channel dimensions (fixed length of 25 mm, radii of 0.75–1.5 mm) and melt velocities (25–150 mm s<sup>−1</sup>) were adjusted to observe pressure drop variations (<span><math><mrow><mstyle><mi>Δ</mi></mstyle><msub><mi>P</mi><mtext>en</mtext></msub></mrow></math></span>) in a special-designed mold. An equivalent pressure concept (<span><math><mrow><mstyle><mi>Δ</mi></mstyle><msub><mi>P</mi><mtext>vis</mtext></msub></mrow></math></span>) was proposed to assess temperature variations induced by viscous dissipation. Dimensionless indices related to channel dimensions (<span><math><msub><mi>I</mi><mrow><mi>P</mi><mo>_</mo><mi>R</mi></mrow></msub></math></span> and <span><math><msub><mi>I</mi><mrow><mtext>Pcor</mtext><mo>_</mo><mi>R</mi></mrow></msub></math></span>) and melt injection velocities (<span><math><msub><mi>I</mi><mrow><mi>P</mi><mo>_</mo><mi>v</mi></mrow></msub></math></span> and <span><math><msub><mi>I</mi><mrow><mtext>Pcor</mtext><mo>_</mo><mi>v</mi></mrow></msub></math></span>) were established to observe pressure drop (<span><math><mrow><mstyle><mi>Δ</mi></mstyle><msub><mi>P</mi><mtext>en</mtext></msub></mrow></math></span>) and corrected pressure drop (<span><math><mrow><mstyle><mi>Δ</mi></mstyle><msub><mi>P</mi><mtext>cor</mtext></msub></mrow></math></span>). The results indicate that the corrected pressure drop and viscosity curves (<span><math><mrow><mstyle><mi>Δ</mi></mstyle><msub><mi>P</mi><mtext>cor</mtext></msub></mrow></math></span> and <span><math><msub><mi>η</mi><mtext>cor</mtext></msub></math></span>) show more consistent variations versus channel dimensions and melt velocities when the viscous dissipation effect is quantitatively incorporated into melt pressure and viscosity analyses (<span><math><mrow><mstyle><mi>Δ</mi></mstyle><msub><mi>P</mi><mtext>en</mtext></msub></mrow></math></span> and <span><math><mi>η</mi></math></span>), aligning closely with observations under adiabatic conditions. Thermal-related dimensionless numbers (Eckert, Brinkman, and Peclet numbers) qualitatively confirm the significance of viscous dissipation. This study offers a comprehensive analysis and validation of thermal effects in mold, presenting a novel method for exploring specific melt behaviors and advancing the analysis of mold interiors in non-adiabatic environments.</div></div","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"336 ","pages":"Article 105378"},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143153117","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 : 2025-02-01Epub Date: 2024-12-24DOI: 10.1016/j.jnnfm.2024.105380
Evgeniy Boyko
Viscous flows through configurations fabricated from soft materials exert stresses at the solid–liquid interface, leading to a coupling between the flow field and the elastic deformation. The resulting fluid–structure interaction affects the relationship between the pressure drop and the flow rate , or the corresponding flow resistance . While the flow resistance in deformable configurations has been extensively studied for Newtonian fluids, it remains largely unexplored for non-Newtonian fluids even at low Reynolds numbers. We analyze the steady low-Reynolds-number fluid–structure interaction between the flow of a non-Newtonian fluid and a deformable tube. We present a theoretical framework for calculating the leading-order effect of the complex fluid rheology and wall compliance on the flow resistance, which holds for a wide class of non-Newtonian constitutive models. For the weakly non-Newtonian limit, our theory provides the first-order non-Newtonian correction for the flow resistance solely using the known Newtonian solution for a deformable tube, bypassing the detailed calculations of the non-Newtonian fluid–structure-interaction problem. We illustrate our approach for a weakly viscoelastic Oldroyd-B fluid and a weakly shear-thinning Carreau fluid. In particular, we show analytically that both the viscoelasticity and shear thinning of the fluid and the compliance of the deformable tube decrease the flow resistance in the weakly non-Newtonian limit and identify the physical mechanisms governing this reduction.
{"title":"Interplay between complex fluid rheology and wall compliance in the flow resistance of deformable axisymmetric configurations","authors":"Evgeniy Boyko","doi":"10.1016/j.jnnfm.2024.105380","DOIUrl":"10.1016/j.jnnfm.2024.105380","url":null,"abstract":"<div><div>Viscous flows through configurations fabricated from soft materials exert stresses at the solid–liquid interface, leading to a coupling between the flow field and the elastic deformation. The resulting fluid–structure interaction affects the relationship between the pressure drop <span><math><mrow><mi>Δ</mi><mi>p</mi></mrow></math></span> and the flow rate <span><math><mi>q</mi></math></span>, or the corresponding flow resistance <span><math><mrow><mi>Δ</mi><mi>p</mi><mo>/</mo><mi>q</mi></mrow></math></span>. While the flow resistance in deformable configurations has been extensively studied for Newtonian fluids, it remains largely unexplored for non-Newtonian fluids even at low Reynolds numbers. We analyze the steady low-Reynolds-number fluid–structure interaction between the flow of a non-Newtonian fluid and a deformable tube. We present a theoretical framework for calculating the leading-order effect of the complex fluid rheology and wall compliance on the flow resistance, which holds for a wide class of non-Newtonian constitutive models. For the weakly non-Newtonian limit, our theory provides the first-order non-Newtonian correction for the flow resistance solely using the known Newtonian solution for a deformable tube, bypassing the detailed calculations of the non-Newtonian fluid–structure-interaction problem. We illustrate our approach for a weakly viscoelastic Oldroyd-B fluid and a weakly shear-thinning Carreau fluid. In particular, we show analytically that both the viscoelasticity and shear thinning of the fluid and the compliance of the deformable tube decrease the flow resistance in the weakly non-Newtonian limit and identify the physical mechanisms governing this reduction.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"336 ","pages":"Article 105380"},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143153119","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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