Pub Date : 2025-09-03DOI: 10.1016/j.jnnfm.2025.105486
Yan Xia , Zhaosheng Yu , Xiao Hu , Chenlin Zhu , Zhaowu Lin
In this work, we numerically investigate the hydrodynamic interactions between two active particles (modeled as squirmers) in a Bingham yield stress fluid, and quantify the influence of the Bingham number and squirmer type on reorientation and scattering in face-to-face and crossing configurations. In the face-to-face configuration, increased Bingham number leads to greater reorientation of neutral and puller-type squirmers. In crossing interactions, yield stress suppresses the strong deflection observed in Newtonian fluids at small incidence angles. In contrast, for larger initial angles, the final separation angle between the squirmers is significantly increased in a yield stress fluid compared to that in a Newtonian fluid. To elucidate the underlying mechanism, we compute hydrodynamic torques on particles by constraining their orientations while allowing translation. In the face-to-face configuration, we find that yield stress amplifies the near-field torques on each particle, driving them to rotate away from one another and thereby increasing scattering. In the side-by-side configuration, yield stress qualitatively alters the sign and magnitude of the hydrodynamic torque on neutral and puller-type squirmers, reducing their tendency to rotate away and thereby favoring sustained parallel swimming. These results provide insight into the rheological behavior and transport properties of active suspensions in complex fluids.
{"title":"Pairwise interactions of active particles in a yield stress fluid","authors":"Yan Xia , Zhaosheng Yu , Xiao Hu , Chenlin Zhu , Zhaowu Lin","doi":"10.1016/j.jnnfm.2025.105486","DOIUrl":"10.1016/j.jnnfm.2025.105486","url":null,"abstract":"<div><div>In this work, we numerically investigate the hydrodynamic interactions between two active particles (modeled as squirmers) in a Bingham yield stress fluid, and quantify the influence of the Bingham number and squirmer type on reorientation and scattering in face-to-face and crossing configurations. In the face-to-face configuration, increased Bingham number leads to greater reorientation of neutral and puller-type squirmers. In crossing interactions, yield stress suppresses the strong deflection observed in Newtonian fluids at small incidence angles. In contrast, for larger initial angles, the final separation angle between the squirmers is significantly increased in a yield stress fluid compared to that in a Newtonian fluid. To elucidate the underlying mechanism, we compute hydrodynamic torques on particles by constraining their orientations while allowing translation. In the face-to-face configuration, we find that yield stress amplifies the near-field torques on each particle, driving them to rotate away from one another and thereby increasing scattering. In the side-by-side configuration, yield stress qualitatively alters the sign and magnitude of the hydrodynamic torque on neutral and puller-type squirmers, reducing their tendency to rotate away and thereby favoring sustained parallel swimming. These results provide insight into the rheological behavior and transport properties of active suspensions in complex fluids.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"345 ","pages":"Article 105486"},"PeriodicalIF":2.8,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003979","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 : 2025-09-01DOI: 10.1016/j.jnnfm.2025.105487
Panagiotis Sialmas, Kostas D. Housiadas
Under the classic lubrication approximation, we develop a unified framework for evaluating the pressure gradient of an incompressible, isothermal viscoelastic fluid in a symmetric channel with slowly varying geometry, including inertia. Exploiting the independence of the pressure gradient from the wall-normal coordinate—a property absent in general 2D planar or 3D axisymmetric flows—we derive multiple integral expressions for the pressure gradient and the corresponding average pressure drop required to maintain a constant flow rate. The derivations use the momentum balance formulated via the extra-stress tensor, providing a flexible, formal, and rigorous procedure, and the physical significance of each expression is discussed.
To bypass choosing among these expressions, we introduce a new set of lubrication equations based on a streamfunction, mapped coordinates, and transformed polymer extra-stress components. This formulation automatically satisfies the continuity equation, the constraints due to fluid incompressibility, the boundary conditions, and the flow symmetries, allowing the pressure gradient to be determined a posteriori and providing a tool for consistency and accuracy checks.
The equivalence of the integral expressions is illustrated in two representative cases: (i) Newtonian inertial flow in a linearly contracting channel, and (ii) viscoelastic inertialess flow in a hyperbolic contraction. In both cases, the predicted average pressure drop agrees very well with high-order asymptotic solutions post-processed via Padé approximants, high-accuracy spectral simulations, and DNS results from the literature. The framework provides a rigorous, general, and computationally robust tool for analyzing lubrication flows of viscoelastic fluids and can be easily extended to other complex fluids and broader flow conditions.
{"title":"General evaluation of the pressure gradient for lubrication flows in varying channels with applications to linear and hyperbolic contractions","authors":"Panagiotis Sialmas, Kostas D. Housiadas","doi":"10.1016/j.jnnfm.2025.105487","DOIUrl":"10.1016/j.jnnfm.2025.105487","url":null,"abstract":"<div><div>Under the classic lubrication approximation, we develop a unified framework for evaluating the pressure gradient of an incompressible, isothermal viscoelastic fluid in a symmetric channel with slowly varying geometry, including inertia. Exploiting the independence of the pressure gradient from the wall-normal coordinate—a property absent in general 2D planar or 3D axisymmetric flows—we derive multiple integral expressions for the pressure gradient and the corresponding average pressure drop required to maintain a constant flow rate. The derivations use the momentum balance formulated via the extra-stress tensor, providing a flexible, formal, and rigorous procedure, and the physical significance of each expression is discussed.</div><div>To bypass choosing among these expressions, we introduce a new set of lubrication equations based on a streamfunction, mapped coordinates, and transformed polymer extra-stress components. This formulation automatically satisfies the continuity equation, the constraints due to fluid incompressibility, the boundary conditions, and the flow symmetries, allowing the pressure gradient to be determined <em>a posteriori</em> and providing a tool for consistency and accuracy checks.</div><div>The equivalence of the integral expressions is illustrated in two representative cases: (i) Newtonian inertial flow in a linearly contracting channel, and (ii) viscoelastic inertialess flow in a hyperbolic contraction. In both cases, the predicted average pressure drop agrees very well with high-order asymptotic solutions post-processed via Padé approximants, high-accuracy spectral simulations, and DNS results from the literature. The framework provides a rigorous, general, and computationally robust tool for analyzing lubrication flows of viscoelastic fluids and can be easily extended to other complex fluids and broader flow conditions.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"346 ","pages":"Article 105487"},"PeriodicalIF":2.8,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145061730","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 : 2025-08-25DOI: 10.1016/j.jnnfm.2025.105485
Hossein Rahmani , Ian Frigaard
We explore the relationship between a yield stress fluid flow in a Hele-Shaw cell with irregular walls, and a non-Darcy 2D porous medium flow with limiting pressure gradient. The continuum (Hele-Shaw) flow is a much-studied simplification of a cementing displacement flow model, solved via a variational formulation that leads to a convex streamfunction minimization problem. Our interest is with the analogy between the discretization used for the numerical solution and network flows that model the associated porous media flow, i.e. via the pore-throat approach. A staggered mesh, with pressure nodes at the cell corners and streamfunction nodes at the cell center is used for the continuum problem, which naturally separates into a network representation comprising primal and dual graphs, linking streamfunction and pressure nodes, respectively. We show explicitly how the continuum model defines a network model and vice versa. We develop the variational form of the network flow, including an appropriate (discrete) streamfunction minimization and a discrete version of the principle of virtual work.
Two network models are explored, based on different interpretations of the minimization problem. The network flow results are compared with analogous computed continuum flow results in 3 specific geometries. We find that our network model I, which is the most natural interpretation of the continuum model as a network flow using our discretization, generally under-predicts flow rates. This is problematic from the perspective of considering the network flow as an approximation to the porous media or Hele-Shaw flow. Network model II rectifies this situation, via a pressure interpolation method. In our examples we find that the network II flow converges to the continuum flow as the mesh and network are refined. This is not the usual comparison made, as in many pore-throat models the network is fixed according to the underlying pore-space geometry. Despite the differences, both network models have their own advantages and disadvantages. Network model I offers a more natural way of modeling the flow and is easier to apply, for example to complex meshes, e.g. unstructured triangular. Network model II gives the more accurate physical representation of the Hele-Shaw flow. Lastly, we have developed approximate algebraic relationships for the total flow rate as a function of the total applied pressure gradient, both close to the critical onset pressure and for large pressure gradients. These correlations align well with previous findings for Bingham fluid flows in porous media.
{"title":"Pore-network modeling of viscoplastic flows: Exploring the Hele-Shaw cell flow analogy","authors":"Hossein Rahmani , Ian Frigaard","doi":"10.1016/j.jnnfm.2025.105485","DOIUrl":"10.1016/j.jnnfm.2025.105485","url":null,"abstract":"<div><div>We explore the relationship between a yield stress fluid flow in a Hele-Shaw cell with irregular walls, and a non-Darcy 2D porous medium flow with limiting pressure gradient. The continuum (Hele-Shaw) flow is a much-studied simplification of a cementing displacement flow model, solved via a variational formulation that leads to a convex streamfunction minimization problem. Our interest is with the analogy between the discretization used for the numerical solution and network flows that model the associated porous media flow, i.e. via the pore-throat approach. A staggered mesh, with pressure nodes at the cell corners and streamfunction nodes at the cell center is used for the continuum problem, which naturally separates into a network representation comprising primal and dual graphs, linking streamfunction and pressure nodes, respectively. We show explicitly how the continuum model defines a network model and vice versa. We develop the variational form of the network flow, including an appropriate (discrete) streamfunction minimization and a discrete version of the principle of virtual work.</div><div>Two network models are explored, based on different interpretations of the minimization problem. The network flow results are compared with analogous computed continuum flow results in 3 specific geometries. We find that our network model I, which is the most natural interpretation of the continuum model as a network flow using our discretization, generally under-predicts flow rates. This is problematic from the perspective of considering the network flow as an approximation to the porous media or Hele-Shaw flow. Network model II rectifies this situation, via a pressure interpolation method. In our examples we find that the network II flow converges to the continuum flow as the mesh and network are refined. This is not the usual comparison made, as in many pore-throat models the network is fixed according to the underlying pore-space geometry. Despite the differences, both network models have their own advantages and disadvantages. Network model I offers a more natural way of modeling the flow and is easier to apply, for example to complex meshes, e.g. unstructured triangular. Network model II gives the more accurate physical representation of the Hele-Shaw flow. Lastly, we have developed approximate algebraic relationships for the total flow rate as a function of the total applied pressure gradient, both close to the critical onset pressure and for large pressure gradients. These correlations align well with previous findings for Bingham fluid flows in porous media.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"345 ","pages":"Article 105485"},"PeriodicalIF":2.8,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144917815","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 : 2025-08-25DOI: 10.1016/j.jnnfm.2025.105484
Fanji Sun , Bo Guo , Luqi Cao , Yuke Li , Xinhui Si
This study numerically investigates viscoelastic flow dynamics around a cylinder near a flat wall using the Giesekus model in OpenFOAM. For the boundary layer on the flat wall, both elastic and shear-thinning properties reduce boundary layer thickness. The coupled elastic and shear-thinning effects of the Giesekus fluid flow around the near-walled cylinders are analyzed through systematic parameters. At high mobility factor, increasing the Weissenberg number primarily enhances the shear-thinning effect, leading to intensified drag and lift fluctuations. However, at low mobility factor, it mainly strengthens the elastic effect, evidenced by the elongation of recirculation zone in the wake. The comparative simulations using the Carcarau model further reveal the competing flow mechanisms between flow stabilization due to elasticity and destabilization caused by shear thinning. In addition to the fluid property parameters, smaller gap ratios enhance flow stability by maintaining lower flow velocity in the gap. Conversely, larger gap ratios increase the velocity, causing high-momentum fluid flow through the gap to deflect and interact with the shear layer formed by the cylinder’s upper wake, thereby triggering vortex shedding. Similarly, a reduced flow development length accelerates the flow velocity in the gap and thins the boundary layer of the plat wall, which promotes flow instability. Both larger gap ratios and shorter development lengths increase the drag and alter the lift direction.
{"title":"Numerical investigation of viscoelastic flow characteristics: Giesekus fluid past a circular cylinder near a flat wall","authors":"Fanji Sun , Bo Guo , Luqi Cao , Yuke Li , Xinhui Si","doi":"10.1016/j.jnnfm.2025.105484","DOIUrl":"10.1016/j.jnnfm.2025.105484","url":null,"abstract":"<div><div>This study numerically investigates viscoelastic flow dynamics around a cylinder near a flat wall using the Giesekus model in OpenFOAM. For the boundary layer on the flat wall, both elastic and shear-thinning properties reduce boundary layer thickness. The coupled elastic and shear-thinning effects of the Giesekus fluid flow around the near-walled cylinders are analyzed through systematic parameters. At high mobility factor, increasing the Weissenberg number primarily enhances the shear-thinning effect, leading to intensified drag and lift fluctuations. However, at low mobility factor, it mainly strengthens the elastic effect, evidenced by the elongation of recirculation zone in the wake. The comparative simulations using the Carcarau model further reveal the competing flow mechanisms between flow stabilization due to elasticity and destabilization caused by shear thinning. In addition to the fluid property parameters, smaller gap ratios enhance flow stability by maintaining lower flow velocity in the gap. Conversely, larger gap ratios increase the velocity, causing high-momentum fluid flow through the gap to deflect and interact with the shear layer formed by the cylinder’s upper wake, thereby triggering vortex shedding. Similarly, a reduced flow development length accelerates the flow velocity in the gap and thins the boundary layer of the plat wall, which promotes flow instability. Both larger gap ratios and shorter development lengths increase the drag and alter the lift direction.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"345 ","pages":"Article 105484"},"PeriodicalIF":2.8,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144895884","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 : 2025-08-20DOI: 10.1016/j.jnnfm.2025.105483
A. Beitollahi , H. Alamdari , S.M. Taghavi
The capillary-driven penetration of non-Newtonian fluids in capillaries with irregular walls is crucial in industrial applications, such as anode manufacturing for aluminum production, where a mixture of coal-tar pitch and fine petroleum coke particles (binder matrix) impregnates the open pores of coarse coke particles. Our study presents a semi-analytical model for capillary-driven flow of shear-thinning fluids in axially varying, wavy-walled microchannels, representative of coke open pore geometries. Incorporating weak inertia, viscous dissipation, and dynamic contact angle behavior (governed by a molecular kinetic theory), the model is systematically derived using lubrication theory and a power-law rheology, yielding a reduced-order equation for the advancing meniscus. The model is validated and calibrated via computational fluid dynamics simulations to extract the dynamic contact angle correction parameter. Our analysis quantifies three distinct penetration regimes and their transition dynamics: inertia-dominated, interfacial dissipation-dominated, and viscous dissipation-dominated. Analytical scaling laws and regime transition correlations are validated across varying power-law indices, Laplace numbers, contact angles, and geometrical features. The power-law index most strongly influences penetration, followed by static contact angle and geometric phase shift, while Laplace number affects early-time behavior. Dynamic contact angle analysis highlights the critical role of interfacial dissipation in irregular geometries. Applied to binder matrices with measured rheology, the model shows that increased fine coke content or channel irregularity significantly delays impregnation.
{"title":"Penetration dynamics of non-Newtonian fluids into axially varying capillaries","authors":"A. Beitollahi , H. Alamdari , S.M. Taghavi","doi":"10.1016/j.jnnfm.2025.105483","DOIUrl":"10.1016/j.jnnfm.2025.105483","url":null,"abstract":"<div><div>The capillary-driven penetration of non-Newtonian fluids in capillaries with irregular walls is crucial in industrial applications, such as anode manufacturing for aluminum production, where a mixture of coal-tar pitch and fine petroleum coke particles (binder matrix) impregnates the open pores of coarse coke particles. Our study presents a semi-analytical model for capillary-driven flow of shear-thinning fluids in axially varying, wavy-walled microchannels, representative of coke open pore geometries. Incorporating weak inertia, viscous dissipation, and dynamic contact angle behavior (governed by a molecular kinetic theory), the model is systematically derived using lubrication theory and a power-law rheology, yielding a reduced-order equation for the advancing meniscus. The model is validated and calibrated via computational fluid dynamics simulations to extract the dynamic contact angle correction parameter. Our analysis quantifies three distinct penetration regimes and their transition dynamics: inertia-dominated, interfacial dissipation-dominated, and viscous dissipation-dominated. Analytical scaling laws and regime transition correlations are validated across varying power-law indices, Laplace numbers, contact angles, and geometrical features. The power-law index most strongly influences penetration, followed by static contact angle and geometric phase shift, while Laplace number affects early-time behavior. Dynamic contact angle analysis highlights the critical role of interfacial dissipation in irregular geometries. Applied to binder matrices with measured rheology, the model shows that increased fine coke content or channel irregularity significantly delays impregnation.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"345 ","pages":"Article 105483"},"PeriodicalIF":2.8,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145018415","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 : 2025-08-18DOI: 10.1016/j.jnnfm.2025.105481
Gláucio Kenji Matoba , Daiane Mieko Iceri , Helder Lima de Moura , Roney Leon Thompson , Annie Fidel-Dufour , Thierry Palermo , Marcelo Souza de Castro
Non-Newtonian fluids, widely utilized in industries such as cosmetics, food processing, and petroleum, exhibit shear-dependent viscosity, necessitating precise rheological characterization for effective pipeline and equipment design. In the petroleum industry, for instance, oils can transition from Newtonian to non-Newtonian behavior under specific conditions, such as long-distance horizontal flow at high pressures and low temperatures (near crystallization). In these cases, oils often behave as viscoplastic fluids, requiring a minimum shear stress, known as yield stress, to initiate flow. The Herschel–Bulkley model is a well-established equation for describing the viscous behavior of such fluids through three rheological parameters: yield stress, power-law index, and consistency coefficient. The determination of these parameters is essential for computing flow characteristics, friction factors, and pressure drops—crucial for designing efficient transport systems. This study aims to characterize a viscoplastic fluid by determining its rheological properties from rheometric and in-situ measurements. To accomplish this, an experimental setup was developed using a model fluid prepared from an aqueous Carbopol and triethanolamine (neutralizing agent) solution. In addition to traditional rheometry, an in-situ approach was evaluated, integrating Particle Image Velocimetry (PIV) with differential pressure sensor data. The velocity profiles obtained enabled the reconstruction of shear rate profiles, while pressure drop data facilitated shear stress profile determination, allowing a flow curve reconstruction. Furthermore, the modified SoFA model (Suspension of Fractal Aggregates) was applied, utilizing Carbopol and Triethanolamine concentrations to estimate the rheological parameters and obtain the corresponding flow curve. A comparative analysis was conducted between serrated parallel-plate rheometry and the PIV–pressure drop method in a commercial 2 inch (0.053 m) pipeline under laminar flow of the aqueous Carbopol solution. The results confirmed that the Herschel–Bulkley model effectively fit the flow curves across all methodologies, with yield stress values deviating by less than 15%. However, consistency indices () obtained from PIV data were overestimated, likely due to the limited shear rate range at the low mean velocities tested. This study highlights the importance of integrating traditional rheometry with in-situ techniques for a comprehensive rheological characterization.
非牛顿流体广泛应用于化妆品、食品加工和石油等行业，具有剪切依赖粘度，因此需要精确的流变特性来进行有效的管道和设备设计。例如，在石油工业中，油在特定条件下可以从牛顿态转变为非牛顿态，例如在高压低温（接近结晶）下的长距离水平流动。在这些情况下，油通常表现为粘塑性流体，需要最小的剪切应力（即屈服应力）来启动流动。Herschel-Bulkley模型是一个成熟的方程，它通过三个流变参数来描述这种流体的粘性行为：屈服应力、幂律指数和一致性系数。这些参数的确定对于计算流动特性、摩擦系数和压降至关重要，对于设计高效的输送系统至关重要。本研究旨在通过流变学和原位测量来确定粘塑性流体的流变特性。为了实现这一目标，开发了一个实验装置，使用由卡波波尔和三乙醇胺（中和剂）水溶液制备的模型流体。除了传统的流变法外，还评估了一种原位方法，将颗粒图像测速（PIV）与差压传感器数据相结合。获得的速度剖面可以重建剪切速率剖面，而压降数据有助于确定剪切应力剖面，从而可以重建流动曲线。采用改进的SoFA （Suspension of Fractal Aggregates）模型，利用卡波醇和三乙醇胺的浓度对其流变参数进行估计，得到相应的流动曲线。在Carbopol水溶液层流条件下，对2英寸（0.053 m）商用管道中锯齿平行板流变法与piv压降法进行了对比分析。结果证实，Herschel-Bulkley模型有效地拟合了所有方法的流动曲线，屈服应力值偏差小于15%。然而，从PIV数据中获得的一致性指数(K)被高估了，这可能是由于在低平均测试速度下剪切速率范围有限。这项研究强调了将传统流变学与原位技术结合起来进行全面流变学表征的重要性。
{"title":"Evaluating viscoplastic properties with rheometry and PIV measurements in pipeline flows","authors":"Gláucio Kenji Matoba , Daiane Mieko Iceri , Helder Lima de Moura , Roney Leon Thompson , Annie Fidel-Dufour , Thierry Palermo , Marcelo Souza de Castro","doi":"10.1016/j.jnnfm.2025.105481","DOIUrl":"10.1016/j.jnnfm.2025.105481","url":null,"abstract":"<div><div>Non-Newtonian fluids, widely utilized in industries such as cosmetics, food processing, and petroleum, exhibit shear-dependent viscosity, necessitating precise rheological characterization for effective pipeline and equipment design. In the petroleum industry, for instance, oils can transition from Newtonian to non-Newtonian behavior under specific conditions, such as long-distance horizontal flow at high pressures and low temperatures (near crystallization). In these cases, oils often behave as viscoplastic fluids, requiring a minimum shear stress, known as yield stress, to initiate flow. The Herschel–Bulkley model is a well-established equation for describing the viscous behavior of such fluids through three rheological parameters: yield stress, power-law index, and consistency coefficient. The determination of these parameters is essential for computing flow characteristics, friction factors, and pressure drops—crucial for designing efficient transport systems. This study aims to characterize a viscoplastic fluid by determining its rheological properties from rheometric and in-situ measurements. To accomplish this, an experimental setup was developed using a model fluid prepared from an aqueous Carbopol and triethanolamine (neutralizing agent) solution. In addition to traditional rheometry, an in-situ approach was evaluated, integrating Particle Image Velocimetry (PIV) with differential pressure sensor data. The velocity profiles obtained enabled the reconstruction of shear rate profiles, while pressure drop data facilitated shear stress profile determination, allowing a flow curve reconstruction. Furthermore, the modified SoFA model (Suspension of Fractal Aggregates) was applied, utilizing Carbopol and Triethanolamine concentrations to estimate the rheological parameters and obtain the corresponding flow curve. A comparative analysis was conducted between serrated parallel-plate rheometry and the PIV–pressure drop method in a commercial 2<!--> <!-->inch (0.053<!--> <!-->m) pipeline under laminar flow of the aqueous Carbopol solution. The results confirmed that the Herschel–Bulkley model effectively fit the flow curves across all methodologies, with yield stress values deviating by less than 15%. However, consistency indices (<span><math><mi>K</mi></math></span>) obtained from PIV data were overestimated, likely due to the limited shear rate range at the low mean velocities tested. This study highlights the importance of integrating traditional rheometry with in-situ techniques for a comprehensive rheological characterization.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"345 ","pages":"Article 105481"},"PeriodicalIF":2.8,"publicationDate":"2025-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144878664","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 : 2025-08-07DOI: 10.1016/j.jnnfm.2025.105482
G. Esposito, Y. Dimakopoulos, J. Tsamopoulos
We investigate the buoyancy-driven motion of an air bubble rising near a vertical solid wall in an elastoviscoplastic (EVP) fluid using three-dimensional direct numerical simulations. The EVP rheology is modelled via the Saramito-Herschel-Bulkley equation, capturing viscous, elastic, and plastic behaviour. Validation against prior experimental and numerical results for unbounded domains shows excellent agreement. The nearby wall induces a lateral migration to the bubble, with the velocity depending on wall distance, bubble volume, and fluid rheology. For larger bubbles, where inertia dominates, the lateral velocity is consistently positive, indicating persistent wall repulsion, and decreases with increasing wall distance. At long times, both lateral and vertical velocities collapse onto a master curve, depending only on the instantaneous wall distance. In contrast, smaller bubbles, dominated by elastic effects, exhibit a non-monotonic lateral velocity: positive near the wall but negative at larger distances, indicating the existence of an equilibrium lateral position. A parametric study highlights the role of deformability in modulating migration dynamics. More deformable bubbles show enhanced repulsion and rising velocities that depend on terminal shape: large, oblate bubbles rise more slowly due to increased cross section in the direction of flow, while smaller teardrop-shaped bubbles rise more efficiently. Increasing the yield stress strengthens the elastic response, shifting the lateral equilibrium distance closer to the wall. Conversely, decreasing the elastic modulus (softening the medium) increases the terminal velocity and enhances wall repulsion. Finally, variations in initial bubble shape and orientation affect transient deformation but have negligible influence on long-term migration or terminal state.
{"title":"Rising and migration dynamics of an air bubble close to a wall in an elastoviscoplastic fluid","authors":"G. Esposito, Y. Dimakopoulos, J. Tsamopoulos","doi":"10.1016/j.jnnfm.2025.105482","DOIUrl":"10.1016/j.jnnfm.2025.105482","url":null,"abstract":"<div><div>We investigate the buoyancy-driven motion of an air bubble rising near a vertical solid wall in an elastoviscoplastic (EVP) fluid using three-dimensional direct numerical simulations. The EVP rheology is modelled via the Saramito-Herschel-Bulkley equation, capturing viscous, elastic, and plastic behaviour. Validation against prior experimental and numerical results for unbounded domains shows excellent agreement. The nearby wall induces a lateral migration to the bubble, with the velocity depending on wall distance, bubble volume, and fluid rheology. For larger bubbles, where inertia dominates, the lateral velocity is consistently positive, indicating persistent wall repulsion, and decreases with increasing wall distance. At long times, both lateral and vertical velocities collapse onto a master curve, depending only on the instantaneous wall distance. In contrast, smaller bubbles, dominated by elastic effects, exhibit a non-monotonic lateral velocity: positive near the wall but negative at larger distances, indicating the existence of an equilibrium lateral position. A parametric study highlights the role of deformability in modulating migration dynamics. More deformable bubbles show enhanced repulsion and rising velocities that depend on terminal shape: large, oblate bubbles rise more slowly due to increased cross section in the direction of flow, while smaller teardrop-shaped bubbles rise more efficiently. Increasing the yield stress strengthens the elastic response, shifting the lateral equilibrium distance closer to the wall. Conversely, decreasing the elastic modulus (softening the medium) increases the terminal velocity and enhances wall repulsion. Finally, variations in initial bubble shape and orientation affect transient deformation but have negligible influence on long-term migration or terminal state.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"345 ","pages":"Article 105482"},"PeriodicalIF":2.8,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144886963","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 : 2025-08-07DOI: 10.1016/j.jnnfm.2025.105469
M.H. Sari , H. Ahmed , C. Putignano , G. Carbone , L. Biancofiore
We analyze a viscoelastic fluid, modeled by the Oldroyd-B constitutive equation, flowing in a sliding abruptly converging/diverging channel. We have chosen this geometry since it has connections to the typical elastohydrodynamic lubricated (EHL), for which recently (Sarı et al., 2024) have illustrated how a viscoelastic lubricant has a positive effect on the tribological performance by raising load and decreasing friction coefficient. We assume that the channel is thin and the magnitude of the “jump” is small enough allowing to take advantage of the thin film approximation. We observe that the step location is a critical factor for generating viscoelastic pressure due to the positive and constant increase in the volumetric flow rate. Presence of viscoelasticity quantified by the ratio between fluid relaxation time and residence time, called Deborah number. A high Deborah number leads to a significant increment in pressure if the step is close to the inlet, while, if it is close to an outlet, the pressure decreases compared to Newtonian flows. While in most of the work, the pressure at the boundaries (inlet and outlet) is set to zero, we also tested more realistic boundary conditions in which the pressure is equal to the average elastic stress, showing that the two kinds of boundary conditions have a similar qualitative behavior. Lastly, a texture geometry, composed by one converging followed by one diverging steps, is inspected to mimic an EHL profile. We find what is the optimal distance between the steps to maximize the load. The role of the elastic stress in this texture profile is finally discussed.
本文用Oldroyd-B本构方程模拟了一种粘弹性流体，该流体在一个滑动的突然收敛/发散通道中流动。我们之所以选择这种几何结构，是因为它与典型的弹性流体动力润滑（EHL）有联系，最近（sarir et al., 2024）已经说明了粘弹性润滑剂如何通过提高载荷和降低摩擦系数对摩擦学性能产生积极影响。我们假设通道很薄，“跳跃”的幅度足够小，可以利用薄膜近似。我们观察到，台阶位置是产生粘弹性压力的关键因素，因为体积流量不断增加。粘弹性的存在由流体松弛时间与停留时间之比量化，称为黛博拉数。如果阶跃靠近入口，高底波拉数会导致压力显著增加，而如果阶跃靠近出口，则与牛顿流相比压力降低。虽然在大多数工作中，边界（入口和出口）的压力被设置为零，但我们也测试了更现实的边界条件，其中压力等于平均弹性应力，表明两种边界条件具有相似的定性行为。最后，由一个收敛步骤和一个发散步骤组成的纹理几何形状被检查以模拟EHL轮廓。我们找到了使负荷最大化的最优步骤之间的距离。最后讨论了弹性应力在该织构中的作用。
{"title":"The role of viscoelastic stress in an abruptly converging/diverging channel under the thin film approximation","authors":"M.H. Sari , H. Ahmed , C. Putignano , G. Carbone , L. Biancofiore","doi":"10.1016/j.jnnfm.2025.105469","DOIUrl":"10.1016/j.jnnfm.2025.105469","url":null,"abstract":"<div><div>We analyze a viscoelastic fluid, modeled by the Oldroyd-B constitutive equation, flowing in a sliding abruptly converging/diverging channel. We have chosen this geometry since it has connections to the typical elastohydrodynamic lubricated (EHL), for which recently (Sarı et al., 2024) have illustrated how a viscoelastic lubricant has a positive effect on the tribological performance by raising load and decreasing friction coefficient. We assume that the channel is thin and the magnitude of the “jump” is small enough allowing to take advantage of the thin film approximation. We observe that the step location is a critical factor for generating viscoelastic pressure due to the positive and constant increase in the volumetric flow rate. Presence of viscoelasticity quantified by the ratio between fluid relaxation time and residence time, called Deborah number. A high Deborah number leads to a significant increment in pressure if the step is close to the inlet, while, if it is close to an outlet, the pressure decreases compared to Newtonian flows. While in most of the work, the pressure at the boundaries (inlet and outlet) is set to zero, we also tested more realistic boundary conditions in which the pressure is equal to the average elastic stress, showing that the two kinds of boundary conditions have a similar qualitative behavior. Lastly, a texture geometry, composed by one converging followed by one diverging steps, is inspected to mimic an EHL profile. We find what is the optimal distance between the steps to maximize the load. The role of the elastic stress in this texture profile is finally discussed.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"345 ","pages":"Article 105469"},"PeriodicalIF":2.8,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144828746","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 : 2025-08-05DOI: 10.1016/j.jnnfm.2025.105471
Paul F. Salipante , Michael Cromer , Gerardo E. Pradillo , Steven D. Hudson
Viscoelastic flow instabilities limit polymer processing rates. High-speed optical measurements of stress and flow are used to provide insight into the relationships between polymer orientation and flow field that lead to viscoelastic fluctuations and instability. The flow of high-molar-mass polyethylene oxide solutions through a cross-slot geometry transitions from a symmetric flow into an asymmetric flow that continually switches its asymmetric configuration at sufficiently high flow rates. Data was acquired by synchronized particle velocimetry and polarization imaging at sub-ms resolution. Three-dimensional numerical simulations using the Giesekus constitutive model demonstrate similar flow switching behavior. Both experiments and simulations show a growth of flow–polymer misalignment near stagnation points prior to switching of the flow asymmetry direction. The role of polymer misalignment demonstrates the important role of stagnation points in flow fields, and this understanding may suggest ways to improve control of instabilities for more efficient processing.
{"title":"Tracking polymer orientation and flow leading to unsteady cross-slot flow: High-speed imaging and modeling","authors":"Paul F. Salipante , Michael Cromer , Gerardo E. Pradillo , Steven D. Hudson","doi":"10.1016/j.jnnfm.2025.105471","DOIUrl":"10.1016/j.jnnfm.2025.105471","url":null,"abstract":"<div><div>Viscoelastic flow instabilities limit polymer processing rates. High-speed optical measurements of stress and flow are used to provide insight into the relationships between polymer orientation and flow field that lead to viscoelastic fluctuations and instability. The flow of high-molar-mass polyethylene oxide solutions through a cross-slot geometry transitions from a symmetric flow into an asymmetric flow that continually switches its asymmetric configuration at sufficiently high flow rates. Data was acquired by synchronized particle velocimetry and polarization imaging at sub-ms resolution. Three-dimensional numerical simulations using the Giesekus constitutive model demonstrate similar flow switching behavior. Both experiments and simulations show a growth of flow–polymer misalignment near stagnation points prior to switching of the flow asymmetry direction. The role of polymer misalignment demonstrates the important role of stagnation points in flow fields, and this understanding may suggest ways to improve control of instabilities for more efficient processing.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"345 ","pages":"Article 105471"},"PeriodicalIF":2.8,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144895883","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}
We derive two asymptotic expansions with a smooth velocity field for free-surface viscoplastic flows down an inclined plane in the shallow-flow approximation. The first expansion is based on the classical Herschel–Bulkley constitutive law by using asymptotic matching at the interface between the pseudo-plug and the sheared layer. In contrast to previous works, where authors considered only one term in the transition layer, we compute two extra terms to guarantee a smooth transition of the inertial contribution from the sheared layer to the pseudo-plug. However, the terms associated to the transition layer are solutions of nonintegrable equations, thus preventing the potential use of this expansion for deriving a shallow-flow model. The second asymptotic expansion is based on an alternative tensorial extension of the Herschel–Bulkley law, for which the alignment between the yield-stress tensor and the strain-rate tensor is relaxed, while the von Mises criterion is kept. In this case, smooth asymptotic expansions of the velocity field are given by fully analytical expressions. Comparison of these two expansions with experiments shows that both give essentially equivalent and relatively good agreement.
{"title":"Smooth thin-layer asymptotic expansions for free-surface yield-stress flows","authors":"Danila Denisenko, Gaël Loïc Richard, Guillaume Chambon","doi":"10.1016/j.jnnfm.2025.105456","DOIUrl":"10.1016/j.jnnfm.2025.105456","url":null,"abstract":"<div><div>We derive two asymptotic expansions with a smooth velocity field for free-surface viscoplastic flows down an inclined plane in the shallow-flow approximation. The first expansion is based on the classical Herschel–Bulkley constitutive law by using asymptotic matching at the interface between the pseudo-plug and the sheared layer. In contrast to previous works, where authors considered only one term in the transition layer, we compute two extra terms to guarantee a smooth transition of the inertial contribution from the sheared layer to the pseudo-plug. However, the terms associated to the transition layer are solutions of nonintegrable equations, thus preventing the potential use of this expansion for deriving a shallow-flow model. The second asymptotic expansion is based on an alternative tensorial extension of the Herschel–Bulkley law, for which the alignment between the yield-stress tensor and the strain-rate tensor is relaxed, while the von Mises criterion is kept. In this case, smooth asymptotic expansions of the velocity field are given by fully analytical expressions. Comparison of these two expansions with experiments shows that both give essentially equivalent and relatively good agreement.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"344 ","pages":"Article 105456"},"PeriodicalIF":2.8,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144724547","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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