Pub Date : 2025-06-15DOI: 10.1016/j.jnnfm.2025.105445
Jesse J. Taylor-West, Andrew J. Hogg
Stagnation points occur in many configurations, such as flow around blunt objects, flow through a T-junction, and squeeze flow between plates. For viscoplastic fluids, vanishing strain rate at a stagnation point results in regions of stagnant unyielded fluid, or “plugs”. We explore the planar flow of a Bingham fluid in the neighbourhood of a stagnation point in a general flow configuration. When the Bingham number is small, this local problem reduces to the prototypical problem of stagnating flow against an infinite planar boundary, varying only with the stagnation angle with which the flow approaches the boundary. We compute numerical solutions of this idealised problem, using the augmented-Lagrangian algorithm, and determine the geometry of the stagnation-point plug as a function of this stagnation angle. As the angle decreases, the plug becomes larger, is elongated in the flow direction, and becomes increasingly asymmetric. However, for all angles, the plug features a right-angle at its vertex, a result that we demonstrate numerically and prove direct from the model equations. We also show how local stagnation plugs are embedded in global flows, illustrating the results from the specific case studies of recirculating flow in a sharp corner and uniform flow around an elliptic cylinder.
{"title":"Stagnation point flow of a viscoplastic fluid","authors":"Jesse J. Taylor-West, Andrew J. Hogg","doi":"10.1016/j.jnnfm.2025.105445","DOIUrl":"10.1016/j.jnnfm.2025.105445","url":null,"abstract":"<div><div>Stagnation points occur in many configurations, such as flow around blunt objects, flow through a T-junction, and squeeze flow between plates. For viscoplastic fluids, vanishing strain rate at a stagnation point results in regions of stagnant unyielded fluid, or “plugs”. We explore the planar flow of a Bingham fluid in the neighbourhood of a stagnation point in a general flow configuration. When the Bingham number is small, this local problem reduces to the prototypical problem of stagnating flow against an infinite planar boundary, varying only with the stagnation angle with which the flow approaches the boundary. We compute numerical solutions of this idealised problem, using the augmented-Lagrangian algorithm, and determine the geometry of the stagnation-point plug as a function of this stagnation angle. As the angle decreases, the plug becomes larger, is elongated in the flow direction, and becomes increasingly asymmetric. However, for all angles, the plug features a right-angle at its vertex, a result that we demonstrate numerically and prove direct from the model equations. We also show how local stagnation plugs are embedded in global flows, illustrating the results from the specific case studies of recirculating flow in a sharp corner and uniform flow around an elliptic cylinder.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"343 ","pages":"Article 105445"},"PeriodicalIF":2.7,"publicationDate":"2025-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144366714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-06-11DOI: 10.1016/j.jnnfm.2025.105440
Mohammad Tanver Hossain , Wonsik Eom , Arjun Shah , Andrew Lowe , Douglas Fudge , Sameh H. Tawfick , Randy H. Ewoldt
<div><div>The yield stress of a viscoplastic material can stabilize an embedded fluid tunnel against capillarity-induced breakup, enabling remarkable technologies such as embedded 3D printing of intricate, freeform, and small components. However, there is persistent disagreement in the published literature between the observed minimum stable diameter, <span><math><msub><mrow><mi>d</mi></mrow><mrow><mo>min</mo></mrow></msub></math></span>, and the theoretical plastocapillary length <span><math><mrow><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi><mi>c</mi></mrow></msub><mo>=</mo><mn>2</mn><mi>Γ</mi><mo>/</mo><msub><mrow><mi>σ</mi></mrow><mrow><mi>y</mi></mrow></msub></mrow></math></span>, with interfacial tension <span><math><mi>Γ</mi></math></span> and bath yield stress <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mi>y</mi></mrow></msub></math></span>, leading to a prior hypothesis that the apparent surface tension <span><math><mi>Γ</mi></math></span> is much smaller to enforce <span><math><mrow><msub><mrow><mi>d</mi></mrow><mrow><mo>min</mo></mrow></msub><mo>=</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi><mi>c</mi></mrow></msub></mrow></math></span>. Here we introduce and experimentally test a new hypothesis that the critical diameter is set by the dimensionless plastocapaillary number, <span><math><mrow><msub><mrow><mi>Y</mi></mrow><mrow><mi>Γ</mi></mrow></msub><mo>=</mo><msub><mrow><mi>σ</mi></mrow><mrow><mi>y</mi></mrow></msub><mi>d</mi><mo>/</mo><mn>2</mn><mi>Γ</mi></mrow></math></span>, having a non-trivial critical value different than one, <span><math><mrow><msub><mrow><mi>Y</mi></mrow><mrow><mi>Γ</mi><mi>c</mi></mrow></msub><mo>≠</mo><mn>1</mn></mrow></math></span>, and therefore the prior hypothesis of adjusting <span><math><mi>Γ</mi></math></span> to enforce <span><math><mrow><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi><mi>c</mi></mrow></msub><mo>=</mo><msub><mrow><mi>d</mi></mrow><mrow><mo>min</mo></mrow></msub></mrow></math></span> is incorrect. We study several Newtonian inks (uncured polydimethylsiloxane (PDMS), highly refined mineral oil, silicone oil) extruded into a wide range of non-Newtonian viscoplastic bath materials (polyacrylic acid microgels, polysaccharide microgels, nanoclay gel, and micro-organogels). Across this wide parameter space, we observe a critical value of <span><math><mrow><msub><mrow><mi>Y</mi></mrow><mrow><mi>Γ</mi><mi>c</mi></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>21</mn><mo>±</mo><mn>0</mn><mo>.</mo><mn>03</mn></mrow></math></span>. We explain this being less than one by analogy to other critical dimensionless groups with yield stress fluids, such as the gravitational stability of a suspended sphere or bubble, where the yield stress acts upon an effective area larger than the naïve estimate set only by embedded object diameter <span><math><mi>d</mi></math></span>. These results provide a new way to understand and predict the minimum stable diameter of embedded liquid filaments, as in embedded
{"title":"The critical plastocapillary number for a Newtonian liquid filament embedded into a viscoplastic fluid","authors":"Mohammad Tanver Hossain , Wonsik Eom , Arjun Shah , Andrew Lowe , Douglas Fudge , Sameh H. Tawfick , Randy H. Ewoldt","doi":"10.1016/j.jnnfm.2025.105440","DOIUrl":"10.1016/j.jnnfm.2025.105440","url":null,"abstract":"<div><div>The yield stress of a viscoplastic material can stabilize an embedded fluid tunnel against capillarity-induced breakup, enabling remarkable technologies such as embedded 3D printing of intricate, freeform, and small components. However, there is persistent disagreement in the published literature between the observed minimum stable diameter, <span><math><msub><mrow><mi>d</mi></mrow><mrow><mo>min</mo></mrow></msub></math></span>, and the theoretical plastocapillary length <span><math><mrow><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi><mi>c</mi></mrow></msub><mo>=</mo><mn>2</mn><mi>Γ</mi><mo>/</mo><msub><mrow><mi>σ</mi></mrow><mrow><mi>y</mi></mrow></msub></mrow></math></span>, with interfacial tension <span><math><mi>Γ</mi></math></span> and bath yield stress <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mi>y</mi></mrow></msub></math></span>, leading to a prior hypothesis that the apparent surface tension <span><math><mi>Γ</mi></math></span> is much smaller to enforce <span><math><mrow><msub><mrow><mi>d</mi></mrow><mrow><mo>min</mo></mrow></msub><mo>=</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi><mi>c</mi></mrow></msub></mrow></math></span>. Here we introduce and experimentally test a new hypothesis that the critical diameter is set by the dimensionless plastocapaillary number, <span><math><mrow><msub><mrow><mi>Y</mi></mrow><mrow><mi>Γ</mi></mrow></msub><mo>=</mo><msub><mrow><mi>σ</mi></mrow><mrow><mi>y</mi></mrow></msub><mi>d</mi><mo>/</mo><mn>2</mn><mi>Γ</mi></mrow></math></span>, having a non-trivial critical value different than one, <span><math><mrow><msub><mrow><mi>Y</mi></mrow><mrow><mi>Γ</mi><mi>c</mi></mrow></msub><mo>≠</mo><mn>1</mn></mrow></math></span>, and therefore the prior hypothesis of adjusting <span><math><mi>Γ</mi></math></span> to enforce <span><math><mrow><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi><mi>c</mi></mrow></msub><mo>=</mo><msub><mrow><mi>d</mi></mrow><mrow><mo>min</mo></mrow></msub></mrow></math></span> is incorrect. We study several Newtonian inks (uncured polydimethylsiloxane (PDMS), highly refined mineral oil, silicone oil) extruded into a wide range of non-Newtonian viscoplastic bath materials (polyacrylic acid microgels, polysaccharide microgels, nanoclay gel, and micro-organogels). Across this wide parameter space, we observe a critical value of <span><math><mrow><msub><mrow><mi>Y</mi></mrow><mrow><mi>Γ</mi><mi>c</mi></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>21</mn><mo>±</mo><mn>0</mn><mo>.</mo><mn>03</mn></mrow></math></span>. We explain this being less than one by analogy to other critical dimensionless groups with yield stress fluids, such as the gravitational stability of a suspended sphere or bubble, where the yield stress acts upon an effective area larger than the naïve estimate set only by embedded object diameter <span><math><mi>d</mi></math></span>. These results provide a new way to understand and predict the minimum stable diameter of embedded liquid filaments, as in embedded","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"343 ","pages":"Article 105440"},"PeriodicalIF":2.7,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144322765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-06-09DOI: 10.1016/j.jnnfm.2025.105442
Shabina Ashraf , Karan Gupta
Imbibition of wetting fluids in confined pore spaces is a ubiquitous phenomenon in nature. Several attempts have been made to understand the invasion of Newtonian fluids in capillaries. The imbibition of non-Newtonian fluids, however, is relatively less explored owing to the dynamic shear rate during the imbibition process. In this work, we develop equations governing the displacement of one power-law fluid with another power-law fluid in axially diverging and converging capillaries. Using lubrication approximation, the governing equations in one-dimension are developed to model the advancing interface with time for various combinations of shear-thinning, shear-thickening, and Newtonian fluids. For this imbibition phenomenon, we explore the effect of imbibing and residing fluid power-law indices, their time scales, interfacial properties, and the impact of the geometric parameters. The developed equations serve as a comprehensive mathematical model, and the self-imbibition relations available in literature can be retrieved from the developed model by considering special cases. We also identify early and late regimes of flow where the viscous resistance of either the imbibing or the residing fluid dominates the imbibition. This study will help design geometrical parameters for pore space with desired flow properties, and has wide applications in microfluidics.
{"title":"Spontaneous imbibition of power-law fluids in filled capillaries of axially varying geometries","authors":"Shabina Ashraf , Karan Gupta","doi":"10.1016/j.jnnfm.2025.105442","DOIUrl":"10.1016/j.jnnfm.2025.105442","url":null,"abstract":"<div><div>Imbibition of wetting fluids in confined pore spaces is a ubiquitous phenomenon in nature. Several attempts have been made to understand the invasion of Newtonian fluids in capillaries. The imbibition of non-Newtonian fluids, however, is relatively less explored owing to the dynamic shear rate during the imbibition process. In this work, we develop equations governing the displacement of one power-law fluid with another power-law fluid in axially diverging and converging capillaries. Using lubrication approximation, the governing equations in one-dimension are developed to model the advancing interface with time for various combinations of shear-thinning, shear-thickening, and Newtonian fluids. For this imbibition phenomenon, we explore the effect of imbibing and residing fluid power-law indices, their time scales, interfacial properties, and the impact of the geometric parameters. The developed equations serve as a comprehensive mathematical model, and the self-imbibition relations available in literature can be retrieved from the developed model by considering special cases. We also identify early and late regimes of flow where the viscous resistance of either the imbibing or the residing fluid dominates the imbibition. This study will help design geometrical parameters for pore space with desired flow properties, and has wide applications in microfluidics.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"343 ","pages":"Article 105442"},"PeriodicalIF":2.7,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144253741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-06-03DOI: 10.1016/j.jnnfm.2025.105437
Fenghui Lin , Zi-Mo Liao , Zhiye Zhao , Nansheng Liu , Xi-Yun Lu , Bamin Khomami
This paper presents an efficient GPU implementation for the direct numerical simulation (DNS) of polymer-induced/modified turbulence, utilizing the open-source finite-difference incompressible Navier–Stokes solver, . The implementation incorporates a versatile viscoelastic solver for two commonly used constitutive equations in DNS of elastic or elastically modified turbulence, namely, the FENE-P and the Giesekus models. Consistent with , the viscoelastic solver uses CUDA Fortran and makes extensive use of kernel loop directives (CUF kernels). To improve the fidelity and robustness of this implementation, a tensor-based interpolation method combined with a shock-capturing WENO scheme is employed for spatial discretization of the polymer constitutive equations. We demonstrate the accuracy and robustness of our code by comparison with existing theoretical and simulation results. In addition, the algorithm exhibits superior scalability with up to eight Nvidia GPU devices in benchmark channel flows. In turn, we use this expeditious code for high-fidelity and efficient large-scale DNS of viscoelastic turbulent flows. To that end, we demonstrate the broad applicability of our implementation in a host of polymer-induced/modified turbulence in channel flows. This includes the maximum drag reduction asymptote, as well as elasto-inertial turbulence, and purely elastic turbulent flows. Overall, this GPU-accelerated simulation technique has all the required ingredients to become the method of choice for large-scale viscoelastic computations aimed at faithfully capturing polymer-induced flow phenomena.
{"title":"GPU acceleration of a hi-fidelity algorithm for direct numerical simulation of polymer-induced/modified turbulence","authors":"Fenghui Lin , Zi-Mo Liao , Zhiye Zhao , Nansheng Liu , Xi-Yun Lu , Bamin Khomami","doi":"10.1016/j.jnnfm.2025.105437","DOIUrl":"10.1016/j.jnnfm.2025.105437","url":null,"abstract":"<div><div>This paper presents an efficient GPU implementation for the direct numerical simulation (DNS) of polymer-induced/modified turbulence, utilizing the open-source finite-difference incompressible Navier–Stokes solver, <span><math><mrow><mi>C</mi><mi>a</mi><mi>N</mi><mi>S</mi></mrow></math></span>. The implementation incorporates a versatile viscoelastic solver for two commonly used constitutive equations in DNS of elastic or elastically modified turbulence, namely, the FENE-P and the Giesekus models. Consistent with <span><math><mrow><mi>C</mi><mi>a</mi><mi>N</mi><mi>S</mi></mrow></math></span>, the viscoelastic solver uses CUDA Fortran and makes extensive use of kernel loop directives (CUF kernels). To improve the fidelity and robustness of this implementation, a tensor-based interpolation method combined with a shock-capturing WENO scheme is employed for spatial discretization of the polymer constitutive equations. We demonstrate the accuracy and robustness of our code by comparison with existing theoretical and simulation results. In addition, the algorithm exhibits superior scalability with up to eight Nvidia GPU devices in benchmark channel flows. In turn, we use this expeditious code for high-fidelity and efficient large-scale DNS of viscoelastic turbulent flows. To that end, we demonstrate the broad applicability of our implementation in a host of polymer-induced/modified turbulence in channel flows. This includes the maximum drag reduction asymptote, as well as elasto-inertial turbulence, and purely elastic turbulent flows. Overall, this GPU-accelerated simulation technique has all the required ingredients to become the method of choice for large-scale viscoelastic computations aimed at faithfully capturing polymer-induced flow phenomena.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"342 ","pages":"Article 105437"},"PeriodicalIF":2.7,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144213217","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}
This paper investigates the relationship between extensional and shear viscosity of low-viscosity power-law fluids. We show the first experimental evidence of the conditions satisfying the same power exponents for extensional and shear viscosity, as indicated by the Carreau model. The extensional and shear viscosity are respectively measured by capillary breakup extensional rheometry dripping-onto-substrate (CaBER-DoS) and by a shear rheometer for various Ohnesorge number . The viscosity ranges measured are about to mPa s for shear viscosity and to mPa s for apparent extensional viscosity. Our experimental results show that, at least for the range of , the power-law expression for the liquid filament radius, apparent extensional viscosity, and shear viscosity holds, even for low-viscosity fluids under our experimental conditions.
{"title":"Experimental study on the relationship between extensional and shear rheology of low-viscosity power-law fluids","authors":"Yuzuki Matsumoto , Misa Kawaguchi , Yoshiyuki Tagawa","doi":"10.1016/j.jnnfm.2025.105436","DOIUrl":"10.1016/j.jnnfm.2025.105436","url":null,"abstract":"<div><div>This paper investigates the relationship between extensional and shear viscosity of low-viscosity power-law fluids. We show the first experimental evidence of the conditions satisfying the same power exponents for extensional and shear viscosity, as indicated by the Carreau model. The extensional and shear viscosity are respectively measured by capillary breakup extensional rheometry dripping-onto-substrate (CaBER-DoS) and by a shear rheometer for various Ohnesorge number <span><math><mrow><mi>O</mi><mi>h</mi></mrow></math></span>. The viscosity ranges measured are about <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>0</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> to <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>4</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> mPa s for shear viscosity and <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>1</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> to <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> mPa s for apparent extensional viscosity. Our experimental results show that, at least for the range of <span><math><mrow><mi>O</mi><mi>h</mi><mo>></mo><mn>1</mn></mrow></math></span>, the power-law expression for the liquid filament radius, apparent extensional viscosity, and shear viscosity holds, even for low-viscosity fluids under our experimental conditions.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"343 ","pages":"Article 105436"},"PeriodicalIF":2.7,"publicationDate":"2025-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144223191","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 : 2025-05-30DOI: 10.1016/j.jnnfm.2025.105438
Gianluca Santesarti , Michele Marino , Francesco Viola , Roberto Verzicco , Giuseppe Vairo
The Carreau–Yasuda rheological model is widely employed in both research and industrial applications to describe the shear-thinning behaviour of non-Newtonian inelastic fluids. However, the model parameter traditionally employed to characterize the shear thinning response exhibits only a weak correlation with the actual shear thinning rate observed in experimental data. This limitation leads to intrinsic identifiability issues, which may result in misleading physical interpretations of the model parameters and unreliable flow predictions. Aiming to contribute to overcoming these issues, this paper introduces a novel heuristic rheological formulation for shear-thinning non-Newtonian inelastic fluids, as an alternative to the Carreau–Yasuda model. Analytical results and exemplary numerical case studies demonstrate that the proposed formulation is based on physically meaningful model parameters, whose identifiability is not compromised by the key limitations of the Carreau–Yasuda model. The new approach allows for effective parameter estimation through a straightforward direct identification strategy, eliminating the need for inverse identification procedures based on nonlinear regression techniques. Moreover, the proposed formulation naturally enables the identication of two Carreau numbers based on the two characteristic shear rates of the fluid.
{"title":"An insight into parameter identifiability issues in the Carreau–Yasuda model: A more consistent rheological formulation for shear-thinning non-Newtonian inelastic fluids","authors":"Gianluca Santesarti , Michele Marino , Francesco Viola , Roberto Verzicco , Giuseppe Vairo","doi":"10.1016/j.jnnfm.2025.105438","DOIUrl":"10.1016/j.jnnfm.2025.105438","url":null,"abstract":"<div><div>The Carreau–Yasuda rheological model is widely employed in both research and industrial applications to describe the shear-thinning behaviour of non-Newtonian inelastic fluids. However, the model parameter traditionally employed to characterize the shear thinning response exhibits only a weak correlation with the actual shear thinning rate observed in experimental data. This limitation leads to intrinsic identifiability issues, which may result in misleading physical interpretations of the model parameters and unreliable flow predictions. Aiming to contribute to overcoming these issues, this paper introduces a novel heuristic rheological formulation for shear-thinning non-Newtonian inelastic fluids, as an alternative to the Carreau–Yasuda model. Analytical results and exemplary numerical case studies demonstrate that the proposed formulation is based on physically meaningful model parameters, whose identifiability is not compromised by the key limitations of the Carreau–Yasuda model. The new approach allows for effective parameter estimation through a straightforward direct identification strategy, eliminating the need for inverse identification procedures based on nonlinear regression techniques. Moreover, the proposed formulation naturally enables the identication of two Carreau numbers based on the two characteristic shear rates of the fluid.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"342 ","pages":"Article 105438"},"PeriodicalIF":2.7,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144204035","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 : 2025-05-30DOI: 10.1016/j.jnnfm.2025.105444
Qiaoyan Ye , Wolfgang Niemeier , Oliver Tiedje , Bo Shen
The present study deals with generalized Newtonian fluids. A method to evaluate the measured extensional viscosity obtained from the pressure drop of entry flow in a capillary die for dilute polymer liquids has been proposed. It is shown that a correction factor based on a calibration curve, which is dependent on the Reynolds number in orifice die, is necessary for the measured entrance pressure drop by using capillary rheometer. The calibration curve for a given orifice die can be derived by using Newtonian test liquids and the Trouton-ratio and applied to determine the extensional viscosity for dilute polymer liquids. Numerical simulations of pressure drop in orifice dies using Newtonian liquids and paint liquids are carried out. The dependence of the proposed correction factor on the Reynolds number can be explained through the analysis of the entry flow field. The Cross model was applied for fitting the measured viscosity curves. A hybrid viscosity model, considering the effects of shear and extensional behaviors, is proposed for the practical applications. Validation between measured and simulated pressure drops in the orifice dies have been performed.
{"title":"Determining extensional viscosity from the measured pressure drop in a capillary rheometer for paint liquids based on fluid dynamic simulations","authors":"Qiaoyan Ye , Wolfgang Niemeier , Oliver Tiedje , Bo Shen","doi":"10.1016/j.jnnfm.2025.105444","DOIUrl":"10.1016/j.jnnfm.2025.105444","url":null,"abstract":"<div><div>The present study deals with generalized Newtonian fluids. A method to evaluate the measured extensional viscosity obtained from the pressure drop of entry flow in a capillary die for dilute polymer liquids has been proposed. It is shown that a correction factor based on a calibration curve, which is dependent on the Reynolds number in orifice die, is necessary for the measured entrance pressure drop by using capillary rheometer. The calibration curve for a given orifice die can be derived by using Newtonian test liquids and the Trouton-ratio and applied to determine the extensional viscosity for dilute polymer liquids. Numerical simulations of pressure drop in orifice dies using Newtonian liquids and paint liquids are carried out. The dependence of the proposed correction factor on the Reynolds number can be explained through the analysis of the entry flow field. The Cross model was applied for fitting the measured viscosity curves. A hybrid viscosity model, considering the effects of shear and extensional behaviors, is proposed for the practical applications. Validation between measured and simulated pressure drops in the orifice dies have been performed.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"343 ","pages":"Article 105444"},"PeriodicalIF":2.7,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144223190","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 : 2025-05-27DOI: 10.1016/j.jnnfm.2025.105435
N. Ali , A.M. Ardekani
The motion of a wavy sheet with time-dependent frequency is discussed in an unbounded non-Newtonian fluid. The rheological behavior of non-Newtonian fluid is captured through the constitutive equation of a second-order fluid. The waves start propagating down the sheet surface with a frequency that achieves a steady-state as an arbitrary function of time. The equation governing the flow is derived under the low Reynolds number approximation. Regular perturbation expansion is employed to develop equations and boundary conditions for stream function at leading and second-order in sheet amplitude. These equations are then solved in Laplace domain to yield expressions of stream functions as arbitrary functions of the frequency of the sheet. Further analysis is carried out for two scenarios. In the first scenario, the sheet is not moving and its undulations produces a net flow. The average velocity of this flow in the horizontal direction is obtained in the Laplace domain. In the second scenario, the sheet is free to move. By employing a force balance at the sheet in the horizontal direction, the swimming velocity of the sheet is also obtained in the Laplace domain. Numerical inversion for some specific choices of sheet frequency is carried out in both scenarios and obtained results are discussed in detail. It is shown that well-behaved pumping and swimming velocities (which are free of jump discontinuity at the initial starting time) for the case in which sheet frequency evolves like a unit-step function are possible in a second-order fluid provided that the amplitudes of longitudinal and transverse waves propagating down the sheet surface satisfy a specific equation.
{"title":"Transient swimming of an undulating sheet in a second-order fluid","authors":"N. Ali , A.M. Ardekani","doi":"10.1016/j.jnnfm.2025.105435","DOIUrl":"10.1016/j.jnnfm.2025.105435","url":null,"abstract":"<div><div>The motion of a wavy sheet with time-dependent frequency is discussed in an unbounded non-Newtonian fluid. The rheological behavior of non-Newtonian fluid is captured through the constitutive equation of a second-order fluid. The waves start propagating down the sheet surface with a frequency that achieves a steady-state as an arbitrary function of time. The equation governing the flow is derived under the low Reynolds number approximation. Regular perturbation expansion is employed to develop equations and boundary conditions for stream function at leading and second-order in sheet amplitude. These equations are then solved in Laplace domain to yield expressions of stream functions as arbitrary functions of the frequency of the sheet. Further analysis is carried out for two scenarios. In the first scenario, the sheet is not moving and its undulations produces a net flow. The average velocity of this flow in the horizontal direction is obtained in the Laplace domain. In the second scenario, the sheet is free to move. By employing a force balance at the sheet in the horizontal direction, the swimming velocity of the sheet is also obtained in the Laplace domain. Numerical inversion for some specific choices of sheet frequency is carried out in both scenarios and obtained results are discussed in detail. It is shown that well-behaved pumping and swimming velocities (which are free of jump discontinuity at the initial starting time) for the case in which sheet frequency evolves like a unit-step function are possible in a second-order fluid provided that the amplitudes of longitudinal and transverse waves propagating down the sheet surface satisfy a specific equation.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"342 ","pages":"Article 105435"},"PeriodicalIF":2.7,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144185713","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 : 2025-05-23DOI: 10.1016/j.jnnfm.2025.105441
Tongsheng Wang , Erik Steur , Tess Homan , Patrick R. Onck , Jaap M.J. den Toonder , Ye Wang
Precise and localized fluid control at small scales is essential for advancing lab-on-a-chip and organ-on-a-chip technologies in fields like biomedicine, drug discovery, and chemical analysis. Traditional pumps are often inadequate for efficient small-volume transport in microfluidic environments, making artificial cilia an appealing solution for integrated, localized fluid management. While magnetically driven cilia offer a biocompatible, non-invasive approach, existing research has primarily focused on Newtonian fluids, leaving the behaviour of shear-thinning fluids largely unexplored. This study investigates the transport characteristics of shear-thinning fluids using a magnetic cilia array under a rotating magnetic field, generating metachronal motion that modulates local viscosity. Results show that the dynamic coupling between cilia beating and the shear‑thinning fluid produces transport behaviour different from that in a Newtonian fluid, particularly at high driving frequencies, offering insights that can inform future design and optimization of magnetic cilia systems for precise fluid control in microfluidic applications, as well as highlighting the importance in studying cilia driven flow in non-Newtonian fluids.
{"title":"The transport characteristics of a shear-thinning fluid driven by metachronal magnetic artificial cilia","authors":"Tongsheng Wang , Erik Steur , Tess Homan , Patrick R. Onck , Jaap M.J. den Toonder , Ye Wang","doi":"10.1016/j.jnnfm.2025.105441","DOIUrl":"10.1016/j.jnnfm.2025.105441","url":null,"abstract":"<div><div>Precise and localized fluid control at small scales is essential for advancing lab-on-a-chip and organ-on-a-chip technologies in fields like biomedicine, drug discovery, and chemical analysis. Traditional pumps are often inadequate for efficient small-volume transport in microfluidic environments, making artificial cilia an appealing solution for integrated, localized fluid management. While magnetically driven cilia offer a biocompatible, non-invasive approach, existing research has primarily focused on Newtonian fluids, leaving the behaviour of shear-thinning fluids largely unexplored. This study investigates the transport characteristics of shear-thinning fluids using a magnetic cilia array under a rotating magnetic field, generating metachronal motion that modulates local viscosity. Results show that the dynamic coupling between cilia beating and the shear‑thinning fluid produces transport behaviour different from that in a Newtonian fluid, particularly at high driving frequencies, offering insights that can inform future design and optimization of magnetic cilia systems for precise fluid control in microfluidic applications, as well as highlighting the importance in studying cilia driven flow in non-Newtonian fluids.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"342 ","pages":"Article 105441"},"PeriodicalIF":2.7,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144170146","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 : 2025-05-19DOI: 10.1016/j.jnnfm.2025.105439
Xi Lin , Qi Li , Yufan Yang , Yan Xing , XiaoHui Lin , Chibin Zhang , Qing Chai
In order to study the profile formation of photoresist microstructure (such as microlens) by the thermal reflow method, the viscoelastic dynamic model is developed based on motion equation, continuity equation, and thin film assumptions. The influence of viscoelastic properties, surface tension, as well as crosslinking effect on polymer melt profile evolution, are considered in this model, and the Oldroyd-B model is used to describe the viscoelastic constitutive relation of polymer melt. Since the viscoelastic dynamic model developed in this paper is a differential equation with regard to the height function of the polymer melt profile, the free surface profile of polymer melts can be obtained naturally during shape evolution by numerically coupling the solution of the film thickness equation and the Oldroyd-B constitutive equation. The computational efficiency of numerical simulation of the free-surface profile would be improved by using this equation as compared to solving the highly non-linear equations of viscoelastic hydrodynamics. The influence of key parameters such as baking time, baking temperature, and crosslinking effect on profile shape evolution is analyzed by this model, and the materials are compared by assigning them different Weissenberg number. In addition, the maximum relative error of verification experiments between the final profile predicted by the simulation and the experimental results is less than 10 %.
{"title":"The viscoelastic dynamic model for profile evolution of photoresist formed during thermal reflow","authors":"Xi Lin , Qi Li , Yufan Yang , Yan Xing , XiaoHui Lin , Chibin Zhang , Qing Chai","doi":"10.1016/j.jnnfm.2025.105439","DOIUrl":"10.1016/j.jnnfm.2025.105439","url":null,"abstract":"<div><div>In order to study the profile formation of photoresist microstructure (such as microlens) by the thermal reflow method, the viscoelastic dynamic model is developed based on motion equation, continuity equation, and thin film assumptions. The influence of viscoelastic properties, surface tension, as well as crosslinking effect on polymer melt profile evolution, are considered in this model, and the Oldroyd-B model is used to describe the viscoelastic constitutive relation of polymer melt. Since the viscoelastic dynamic model developed in this paper is a differential equation with regard to the height function of the polymer melt profile, the free surface profile of polymer melts can be obtained naturally during shape evolution by numerically coupling the solution of the film thickness equation and the Oldroyd-B constitutive equation. The computational efficiency of numerical simulation of the free-surface profile would be improved by using this equation as compared to solving the highly non-linear equations of viscoelastic hydrodynamics. The influence of key parameters such as baking time, baking temperature, and crosslinking effect on profile shape evolution is analyzed by this model, and the materials are compared by assigning them different Weissenberg number. In addition, the maximum relative error of verification experiments between the final profile predicted by the simulation and the experimental results is less than 10 %.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"342 ","pages":"Article 105439"},"PeriodicalIF":2.7,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144124837","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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