Pub Date : 2025-11-19DOI: 10.1016/j.jnnfm.2025.105530
Ian Frigaard
Yield stress fluids have the ability to withstand a shear stress while at rest, i.e. below the yield stress. Consequently, the zero solution has a wider range of application than in Newtonian hydrostatics. Alternatively, one could say that with yield stress fluids a new branch of hydrostatics is possible. This paper shows how in general zero flows are intuitively described using the yield number. It gives the general definition of a critical yield number, above which flows are static. The critical yield number also frequently defines a parametric domain in which the flow is nonlinearly stable, as is demonstrated. The mathematical concepts are introduced from the perspective of a reader who wishes to use a new toolbox and the main ideas are illustrated with a wide range of application flows and examples.
{"title":"U = 0?","authors":"Ian Frigaard","doi":"10.1016/j.jnnfm.2025.105530","DOIUrl":"10.1016/j.jnnfm.2025.105530","url":null,"abstract":"<div><div>Yield stress fluids have the ability to withstand a shear stress while at rest, i.e. below the yield stress. Consequently, the zero solution has a wider range of application than in Newtonian hydrostatics. Alternatively, one could say that with yield stress fluids a new branch of hydrostatics is possible. This paper shows how in general zero flows are intuitively described using the <em>yield</em> number. It gives the general definition of a critical yield number, above which flows are static. The critical yield number also frequently defines a parametric domain in which the flow is nonlinearly stable, as is demonstrated. The mathematical concepts are introduced from the perspective of a reader who wishes to use a new toolbox and the main ideas are illustrated with a wide range of application flows and examples.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"347 ","pages":"Article 105530"},"PeriodicalIF":2.8,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145693987","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 : 2025-11-19DOI: 10.1016/j.jnnfm.2025.105531
Minzun He, Weiyang Jiang, Zijing Ding
This study presents a first-order weighted-residual model for viscoelastic thin-film flow on inverted substrates, incorporating van der Waals interactions. The model is derived via systematic scaling analysis, boundary-layer approximations, and a Galerkin weighted-residual method based on the Oldroyd-B constitutive framework. It achieves a balance between computational efficiency and accurate representation of viscoelastic effects. A notable feature is the ability to independently adjust the Deborah number () and the retardation ratio (), addressing the limitation of Benney-type models that depend only on the combined parameter . The model remains accurate for large . Analysis of the principal dimensionless parameters (, , , , ) clarifies the stability behavior: increasing enhances elastic instability, whereas a larger weakens viscoelastic effects. The cutoff wavenumber depends on gravity (), surface tension (), and van der Waals forces (), but not on or . Validation against linearized Navier–Stokes (LNS) solutions and direct numerical simulations (DNS) shows closer agreement than the Benney-type model, particularly at high . The model also reproduces ultrathin-film rupture via cusp formation induced by van der Waals forces and predicts the scaling law near rupture.
本研究提出了一个考虑范德华相互作用的一阶粘弹性薄膜流动的加权残差模型。该模型通过系统的尺度分析、边界层近似和基于Oldroyd-B本构框架的Galerkin加权残差法得到。它在计算效率和粘弹性效应的准确表示之间取得了平衡。一个显著的特点是能够独立调节Deborah数（De）和延迟比(r)，解决了benney型模型仅依赖于组合参数M=(1−r)De的局限性。对主要无量纲参数（De， S, r， A, Ga）的分析澄清了稳定性行为：增加De会增强弹性不稳定性，而较大的r会减弱粘弹性效应。截止波数kc取决于重力（Ga）、表面张力(S)和范德华力(A)，但与De或r无关。对线性化Navier-Stokes （LNS）解和直接数值模拟（DNS）的验证表明，与benney型模型更接近，特别是在高De时。该模型还通过范德华力诱导的尖点形成再现了超薄膜破裂，并预测了破裂附近的标度律hmin∝(tr−t)1/5。
{"title":"Modeling Rayleigh–Taylor instability in viscoelastic liquid film flow","authors":"Minzun He, Weiyang Jiang, Zijing Ding","doi":"10.1016/j.jnnfm.2025.105531","DOIUrl":"10.1016/j.jnnfm.2025.105531","url":null,"abstract":"<div><div>This study presents a first-order weighted-residual model for viscoelastic thin-film flow on inverted substrates, incorporating van der Waals interactions. The model is derived via systematic scaling analysis, boundary-layer approximations, and a Galerkin weighted-residual method based on the Oldroyd-B constitutive framework. It achieves a balance between computational efficiency and accurate representation of viscoelastic effects. A notable feature is the ability to independently adjust the Deborah number (<span><math><mrow><mi>D</mi><mi>e</mi></mrow></math></span>) and the retardation ratio (<span><math><mi>r</mi></math></span>), addressing the limitation of Benney-type models that depend only on the combined parameter <span><math><mrow><mi>M</mi><mo>=</mo><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mi>r</mi><mo>)</mo></mrow><mi>D</mi><mi>e</mi></mrow></math></span>. The model remains accurate for large <span><math><mrow><mi>D</mi><mi>e</mi></mrow></math></span>. Analysis of the principal dimensionless parameters (<span><math><mrow><mi>D</mi><mi>e</mi></mrow></math></span>, <span><math><mi>S</mi></math></span>, <span><math><mi>r</mi></math></span>, <span><math><mi>A</mi></math></span>, <span><math><mrow><mi>G</mi><mi>a</mi></mrow></math></span>) clarifies the stability behavior: increasing <span><math><mrow><mi>D</mi><mi>e</mi></mrow></math></span> enhances elastic instability, whereas a larger <span><math><mi>r</mi></math></span> weakens viscoelastic effects. The cutoff wavenumber <span><math><msub><mrow><mi>k</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span> depends on gravity (<span><math><mrow><mi>G</mi><mi>a</mi></mrow></math></span>), surface tension (<span><math><mi>S</mi></math></span>), and van der Waals forces (<span><math><mi>A</mi></math></span>), but not on <span><math><mrow><mi>D</mi><mi>e</mi></mrow></math></span> or <span><math><mi>r</mi></math></span>. Validation against linearized Navier–Stokes (LNS) solutions and direct numerical simulations (DNS) shows closer agreement than the Benney-type model, particularly at high <span><math><mrow><mi>D</mi><mi>e</mi></mrow></math></span>. The model also reproduces ultrathin-film rupture via cusp formation induced by van der Waals forces and predicts the scaling law <span><math><mrow><msub><mrow><mi>h</mi></mrow><mrow><mo>min</mo></mrow></msub><mo>∝</mo><msup><mrow><mrow><mo>(</mo><msub><mrow><mi>t</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>−</mo><mi>t</mi><mo>)</mo></mrow></mrow><mrow><mn>1</mn><mo>/</mo><mn>5</mn></mrow></msup></mrow></math></span> near rupture.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"347 ","pages":"Article 105531"},"PeriodicalIF":2.8,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145623770","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 : 2025-11-19DOI: 10.1016/j.jnnfm.2025.105532
Juanyong Wang , Xinyue Liu , Lei Wang , Yuan Yu , Yiran Ji
This study introduces a novel fluctuating lattice Boltzmann (LB) method for simulating viscoelastic fluid flows governed by the Oldroyd-B model. In contrast to conventional LB approaches that explicitly compute the divergence of the polymer stress tensor using finite-difference schemes, the proposed method incorporates the polymer stress implicitly by introducing a polymer stress fluctuation term directly into the evolution equation. This treatment avoids the need for stress-gradient computations, and preserves the physical characteristics of viscoelastic fluid flows. The proposed method is validated against five classical benchmark problems: the simplified four-roll mill, planar Poiseuille flow, unsteady Womersley flow, flow past a cylinder, and the three-dimensional Taylor–Green vortex. The numerical results show excellent agreement with analytical solutions and previous numerical results, confirming the method’s reliability in viscoelastic fluid dynamics. Moreover, performance evaluations demonstrate that the present model reduces the memory occupancy and enhances computational efficiency, highlighting its potential for large-scale simulations of complex viscoelastic flows systems.
{"title":"A fluctuating lattice Boltzmann method for viscoelastic fluid flows","authors":"Juanyong Wang , Xinyue Liu , Lei Wang , Yuan Yu , Yiran Ji","doi":"10.1016/j.jnnfm.2025.105532","DOIUrl":"10.1016/j.jnnfm.2025.105532","url":null,"abstract":"<div><div>This study introduces a novel fluctuating lattice Boltzmann (LB) method for simulating viscoelastic fluid flows governed by the Oldroyd-B model. In contrast to conventional LB approaches that explicitly compute the divergence of the polymer stress tensor using finite-difference schemes, the proposed method incorporates the polymer stress implicitly by introducing a polymer stress fluctuation term directly into the evolution equation. This treatment avoids the need for stress-gradient computations, and preserves the physical characteristics of viscoelastic fluid flows. The proposed method is validated against five classical benchmark problems: the simplified four-roll mill, planar Poiseuille flow, unsteady Womersley flow, flow past a cylinder, and the three-dimensional Taylor–Green vortex. The numerical results show excellent agreement with analytical solutions and previous numerical results, confirming the method’s reliability in viscoelastic fluid dynamics. Moreover, performance evaluations demonstrate that the present model reduces the memory occupancy and enhances computational efficiency, highlighting its potential for large-scale simulations of complex viscoelastic flows systems.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"347 ","pages":"Article 105532"},"PeriodicalIF":2.8,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145579619","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 : 2025-11-11DOI: 10.1016/j.jnnfm.2025.105529
Aidar I. Kadyirov
The importance of extensional rheology to the flow structure in single and double converging-diverging (Cnv-Dvr) pipes has been observed experimentally. The aqueous solutions of 0.1 % polyacrylamide and 0.155 % Xanthan gum with the same shear viscosity but different extensional behavior were chosen as moderately and weakly elastic polymer solutions. For single Cnv-Dvr pipes with conical restriction rate of 2:1:2 it was observed that in a wide range of Weissenberg, Deborah and Reynolds numbers a vortex is generated in converging or diverging sections only, which depends on the type of a polymer solution. Similar tendency was found for double Cnv-Dvr pipes, except that both fluids generate a smaller vortex in the middle section (diverging-converging section). For all runs related to the polymer solution flows and conducted in the present study, the elastic forces predominate over inertial ones. The vortex formation for moderately elastic polymer solutions observed in double Cnv-Dvr pipes like in a single one leads to the axial velocity oscillations with an increase in amplitude with the flow rate up until the critical value. The emerging smaller vortex in the middle section does not change this behavior and oscillates with the same frequency. The location of vortex formation for weakly elastic polymer solution in both pipes is similar to Newtonian fluid.
{"title":"Vortex dynamics in converging-diverging pipes for weakly and moderately elastic polymer solutions","authors":"Aidar I. Kadyirov","doi":"10.1016/j.jnnfm.2025.105529","DOIUrl":"10.1016/j.jnnfm.2025.105529","url":null,"abstract":"<div><div>The importance of extensional rheology to the flow structure in single and double converging-diverging (Cnv-Dvr) pipes has been observed experimentally. The aqueous solutions of 0.1 % polyacrylamide and 0.155 % Xanthan gum with the same shear viscosity but different extensional behavior were chosen as moderately and weakly elastic polymer solutions. For single Cnv-Dvr pipes with conical restriction rate of 2:1:2 it was observed that in a wide range of Weissenberg, Deborah and Reynolds numbers a vortex is generated in converging or diverging sections only, which depends on the type of a polymer solution. Similar tendency was found for double Cnv-Dvr pipes, except that both fluids generate a smaller vortex in the middle section (diverging-converging section). For all runs related to the polymer solution flows and conducted in the present study, the elastic forces predominate over inertial ones. The vortex formation for moderately elastic polymer solutions observed in double Cnv-Dvr pipes like in a single one leads to the axial velocity oscillations with an increase in amplitude with the flow rate up until the critical value. The emerging smaller vortex in the middle section does not change this behavior and oscillates with the same frequency. The location of vortex formation for weakly elastic polymer solution in both pipes is similar to Newtonian fluid.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"347 ","pages":"Article 105529"},"PeriodicalIF":2.8,"publicationDate":"2025-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145529009","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 : 2025-11-10DOI: 10.1016/j.jnnfm.2025.105518
H. Furukawa , S. Iwata , T.N. Phillips , S.J. Lind , M.J. Walters
The dynamics of thin-shell encapsulated microbubbles (EMBs) in viscoelastic fluids forced by ultrasound are investigated in this paper. EMBs, which are gas-filled microbubbles encased in a stiff albumin or flexible lipid shell, have been shown to improve the performance of biomedical procedures such as ultrasound contrast imaging and sonoporation. To gain computationally efficient initial insights, the flow is assumed irrotational and axisymmetric, and is solved via the boundary element method. The viscoelastic fluid is modelled using the Oldroyd B model with both the fluid and the properties of the shell accounted for through the dynamic boundary condition at the bubble surface. A large bubble shell thickness is found to have a significant stabilising effect on the bubble, markedly reducing bubble deformation and response to the ultrasound pulse. For realistic ultrasound and biological fluid parameters, shell properties appear to dominate over fluid rheology. Although at lower shell thicknesses the dynamics are governed by a competition between viscous, elastic and inertial forces. A larger response is observed for lower frequency ultrasound and for pressure amplitudes typical to sonoporation, large translational movement in the direction of the pulse is predicted as well as deformation and the potential for bubble fragmentation. The model and quantitative insights herein have the potential to form the basis of a low-cost computational tool useful for EMB design, fabrication and characterisation in the near future.
{"title":"The influence of viscoelasticity on the dynamics of encapsulated microbubbles near a rigid surface forced by ultrasound","authors":"H. Furukawa , S. Iwata , T.N. Phillips , S.J. Lind , M.J. Walters","doi":"10.1016/j.jnnfm.2025.105518","DOIUrl":"10.1016/j.jnnfm.2025.105518","url":null,"abstract":"<div><div>The dynamics of thin-shell encapsulated microbubbles (EMBs) in viscoelastic fluids forced by ultrasound are investigated in this paper. EMBs, which are gas-filled microbubbles encased in a stiff albumin or flexible lipid shell, have been shown to improve the performance of biomedical procedures such as ultrasound contrast imaging and sonoporation. To gain computationally efficient initial insights, the flow is assumed irrotational and axisymmetric, and is solved via the boundary element method. The viscoelastic fluid is modelled using the Oldroyd B model with both the fluid and the properties of the shell accounted for through the dynamic boundary condition at the bubble surface. A large bubble shell thickness is found to have a significant stabilising effect on the bubble, markedly reducing bubble deformation and response to the ultrasound pulse. For realistic ultrasound and biological fluid parameters, shell properties appear to dominate over fluid rheology. Although at lower shell thicknesses the dynamics are governed by a competition between viscous, elastic and inertial forces. A larger response is observed for lower frequency ultrasound and for pressure amplitudes typical to sonoporation, large translational movement in the direction of the pulse is predicted as well as deformation and the potential for bubble fragmentation. The model and quantitative insights herein have the potential to form the basis of a low-cost computational tool useful for EMB design, fabrication and characterisation in the near future.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"347 ","pages":"Article 105518"},"PeriodicalIF":2.8,"publicationDate":"2025-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145529016","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}
{"title":"Corrigendum to “Natural convection within a non-uniformly heated cavity partly filled with a shear-thinning nanofluid and partly with air” [Journal of Non-Newtonian Fluid Mechanics 289 (2021) 104490]","authors":"Asma Ouahouah , Nabila Labsi , Xavier Chesneau , Youb Khaled Benkahla","doi":"10.1016/j.jnnfm.2025.105516","DOIUrl":"10.1016/j.jnnfm.2025.105516","url":null,"abstract":"","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"347 ","pages":"Article 105516"},"PeriodicalIF":2.8,"publicationDate":"2025-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145747479","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 : 2025-11-05DOI: 10.1016/j.jnnfm.2025.105519
John Hinch
Sialmas & Housiadas (2025), found a similarity solution of the Oldroyd-B equations for viscoelastic flow through a slowly varying axisymmetric contraction with a hyperbolic shape. We study whether inlet stresses decay onto this similarity solution before the end of the pipe, finding they do so only when a strain-rate based Deborah number is sufficiently small, .
{"title":"Approach to a similarity solution of the lubrication flow of an Oldroyd-B fluid through a hyperbolic pipe","authors":"John Hinch","doi":"10.1016/j.jnnfm.2025.105519","DOIUrl":"10.1016/j.jnnfm.2025.105519","url":null,"abstract":"<div><div>Sialmas & Housiadas (2025), found a similarity solution of the Oldroyd-B equations for viscoelastic flow through a slowly varying axisymmetric contraction with a hyperbolic shape. We study whether inlet stresses decay onto this similarity solution before the end of the pipe, finding they do so only when a strain-rate based Deborah number is sufficiently small, <span><math><mrow><mi>D</mi><msub><mrow><mi>e</mi></mrow><mrow><mi>e</mi></mrow></msub><mo>≲</mo><mn>1</mn></mrow></math></span>.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"347 ","pages":"Article 105519"},"PeriodicalIF":2.8,"publicationDate":"2025-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145468551","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 : 2025-11-01DOI: 10.1016/j.jnnfm.2025.105515
G. Barrera , J. Arcos , F. Méndez , O. Bautista
This work theoretically analyzes the influence of the slippage condition on the pulsatile flow of a viscoelastic fluid, whose rheological behavior follows the Jeffreys model, through circular and concentric annular tubes. A pulsatile pressure gradient causes the flow and a dynamic slip model is assumed on the walls of the tube to depend on the past states of the local wall shear stress, similar to the concept of the viscoelastic fluid memory, where the local state of the stress depends on the past deformation history to which the fluid particles are subject Hatzikiriakos (2012). As part of the assumptions, a periodic flow condition is considered, which is defined as the stage when the transient stage has finished. The hydrodynamics is obtained by solving the momentum equation, which is derived from a suitable combination of the Cauchy and Jeffreys constitutive equations, subject to the slip boundary condition that depends on the Jeffreys rheological model. The mathematical model is nondimensionalized, arising parameters that characterize the flow: the Womersley number , the Deborah numbers of the fluid, the slip relaxation number Des associated to the dynamic slip boundary condition; the parameter that represents the ratio between the relaxation and retardation times of the fluid; a parameter representing the ratio between the inner and outer radii of the annular tube; the slip parameters and related to the slippage at the walls. We illustrate the influence of the dimensionless parameters involved in the analysis through phase portrait diagrams that depict the dynamics of the flow. Based on the hydrodynamic field, we determine the instantaneous volumetric flow rate and evaluate the Poiseuille number as a function of the slip relaxation number. Additionally, we develop an asymptotic solution for the hydrodynamic field in the limit where , which aids in understanding the flow dynamics.
{"title":"Friction factor for pulsatile flow of viscoelastic fluids in circular tubes and concentric annuli using a dynamic slip model at the walls","authors":"G. Barrera , J. Arcos , F. Méndez , O. Bautista","doi":"10.1016/j.jnnfm.2025.105515","DOIUrl":"10.1016/j.jnnfm.2025.105515","url":null,"abstract":"<div><div>This work theoretically analyzes the influence of the slippage condition on the pulsatile flow of a viscoelastic fluid, whose rheological behavior follows the Jeffreys model, through circular and concentric annular tubes. A pulsatile pressure gradient causes the flow and a dynamic slip model is assumed on the walls of the tube <em>to depend on the past states of the local wall shear stress, similar to the concept of the viscoelastic fluid memory, where the local state of the stress depends on the past deformation history to which the fluid particles are subject</em> Hatzikiriakos (2012). As part of the assumptions, a periodic flow condition is considered, which is defined as the stage when the transient stage has finished. The hydrodynamics is obtained by solving the momentum equation, which is derived from a suitable combination of the Cauchy and Jeffreys constitutive equations, subject to the slip boundary condition that depends on the Jeffreys rheological model. The mathematical model is nondimensionalized, arising parameters that characterize the flow: the Womersley number <span><math><mi>Wo</mi></math></span>, the Deborah numbers <span><math><mi>De</mi></math></span> of the fluid, the slip relaxation number De<sub>s</sub> associated to the dynamic slip boundary condition; the parameter <span><math><mi>Λ</mi></math></span> that represents the ratio between the relaxation and retardation times of the fluid; a parameter <span><math><mi>κ</mi></math></span> representing the ratio between the inner and outer radii of the annular tube; the slip parameters <span><math><msub><mrow><mi>β</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>β</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> related to the slippage at the walls. We illustrate the influence of the dimensionless parameters involved in the analysis through phase portrait diagrams that depict the dynamics of the flow. Based on the hydrodynamic field, we determine the instantaneous volumetric flow rate and evaluate the Poiseuille number as a function of the slip relaxation number. Additionally, we develop an asymptotic solution for the hydrodynamic field in the limit where <span><math><mrow><mi>Wo</mi><mo>≪</mo><mn>1</mn></mrow></math></span>, which aids in understanding the flow dynamics.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"347 ","pages":"Article 105515"},"PeriodicalIF":2.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145468550","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 : 2025-10-25DOI: 10.1016/j.jnnfm.2025.105517
Noman Yousuf , Daniel Lester , Andrew Chryss , Murray Rudman , Nicky Eshtiaghi
Turbulent pipe flow of generalised Newtonian (GN) fluids is prevalent in many industries. However, outstanding challenges include the accurate prediction of both the pressure gradient (or friction factor Cf) and the Reynolds number Returb which marks the onset of predominantly turbulent pipe flow. Although validated over a limited range of conditions, conventional methods such as empirical correlations and numerical simulations with unvalidated turbulence closures yield large errors when applied outside this range. This study addresses these challenges by using a validated direct numerical simulation (DNS) method for shear-thinning GN turbulent pipe flow, which resolves all spatiotemporal scales of the flow and so does not require turbulence closure. DNS simulations of shear-thinning turbulent pipe flow are used to develop simple and accurate correlations for Returb and Cf for both Herschel-Bulkley (HB) and Sisko rheological models (which capture the behaviour of most shear-thinning GN fluids) over a wide range of flow and rheology parameters. The DNS-based correlations for Cf are found to exhibit superior accuracy (L2 error ∼6 %) compared to most conventional empirical correlations (L2 error ∼16 %). We also demonstrate that these correlations can be used to estimate rheological parameters from combined laminar and turbulent pipe flow data. Hence, these correlations offer a simple, robust and accurate method for prediction of turbulent pipe flow of shear-thinning fluids and estimation of their rheological parameters.
{"title":"Accurate correlations for turbulent pipe flow of shear-thinning fluids","authors":"Noman Yousuf , Daniel Lester , Andrew Chryss , Murray Rudman , Nicky Eshtiaghi","doi":"10.1016/j.jnnfm.2025.105517","DOIUrl":"10.1016/j.jnnfm.2025.105517","url":null,"abstract":"<div><div>Turbulent pipe flow of generalised Newtonian (GN) fluids is prevalent in many industries. However, outstanding challenges include the accurate prediction of both the pressure gradient (or friction factor <em>C<sub>f</sub></em>) and the Reynolds number <em>Re<sub>turb</sub></em> which marks the onset of predominantly turbulent pipe flow. Although validated over a limited range of conditions, conventional methods such as empirical correlations and numerical simulations with unvalidated turbulence closures yield large errors when applied outside this range. This study addresses these challenges by using a validated direct numerical simulation (DNS) method for shear-thinning GN turbulent pipe flow, which resolves all spatiotemporal scales of the flow and so does not require turbulence closure. DNS simulations of shear-thinning turbulent pipe flow are used to develop simple and accurate correlations for <em>Re<sub>turb</sub></em> and <em>C<sub>f</sub></em> for both Herschel-Bulkley (HB) and Sisko rheological models (which capture the behaviour of most shear-thinning GN fluids) over a wide range of flow and rheology parameters. The DNS-based correlations for <em>C<sub>f</sub></em> are found to exhibit superior accuracy (L<sub>2</sub> error ∼6 %) compared to most conventional empirical correlations (L<sub>2</sub> error ∼16 %). We also demonstrate that these correlations can be used to estimate rheological parameters from combined laminar and turbulent pipe flow data. Hence, these correlations offer a simple, robust and accurate method for prediction of turbulent pipe flow of shear-thinning fluids and estimation of their rheological parameters.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"347 ","pages":"Article 105517"},"PeriodicalIF":2.8,"publicationDate":"2025-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145579620","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 : 2025-10-22DOI: 10.1016/j.jnnfm.2025.105514
M. Pourjafar-Chelikdani , G. Biglari , P. Zakeri , K. Sadeghy
Encapsulated spherical gas bubbles are increasingly used as contrast agents in ultrasound imaging. The main restriction is the shear stress that is experienced by the vessel wall during bubble oscillations as it may damage its endothelial cells. Previous attempts to estimate the wall shear stress treated blood as a Newtonian fluid. In the present work, using the Carreau rheological model, we numerically investigate the effect of blood shear-thinning behavior on the wall shear stress. To ensure that the bubble remains nearly spherical during oscillations, simulation is restricted to small amplitudes for the acoustic pulse. To calculate the bubble’s instantaneous radius, we relied on the de Jong’s model for a linearly viscoelastic shell made of the Kelvin–Voigt material. By assuming that the micro-vessel obeys the Hooke’s law, the two-way coupling between the bubble and the vessel is achieved by solving the equations of motions for the liquid medium separating them. Blood shear-thinning is predicted to increase the vessel’s peak shear stress by roughly 30%. Shear-thinning also doubles the frequency corresponding to the peak shear stress. For shear-thinning liquids, the velocity profiles are predicted to contain inflection points suggesting that the flow induced in the liquid is vulnerable to hydrodynamic instability. A parameter study reveals that the time-constant in the Carreau model strongly controls the flow kinematics and dynamics during bubble oscillations. The conclusion is that blood shear-thinning behavior should be considered in cases where bubbles are used as contrast agents.
{"title":"Small-amplitude forced oscillation of encapsulated gas bubbles in elastic microchannels: effect of blood shear-thinning","authors":"M. Pourjafar-Chelikdani , G. Biglari , P. Zakeri , K. Sadeghy","doi":"10.1016/j.jnnfm.2025.105514","DOIUrl":"10.1016/j.jnnfm.2025.105514","url":null,"abstract":"<div><div>Encapsulated spherical gas bubbles are increasingly used as contrast agents in ultrasound imaging. The main restriction is the shear stress that is experienced by the vessel wall during bubble oscillations as it may damage its endothelial cells. Previous attempts to estimate the wall shear stress treated blood as a Newtonian fluid. In the present work, using the Carreau rheological model, we numerically investigate the effect of blood shear-thinning behavior on the wall shear stress. To ensure that the bubble remains nearly spherical during oscillations, simulation is restricted to small amplitudes for the acoustic pulse. To calculate the bubble’s instantaneous radius, we relied on the de Jong’s model for a linearly viscoelastic shell made of the Kelvin–Voigt material. By assuming that the micro-vessel obeys the Hooke’s law, the two-way coupling between the bubble and the vessel is achieved by solving the equations of motions for the liquid medium separating them. Blood shear-thinning is predicted to increase the vessel’s peak shear stress by roughly 30%. Shear-thinning also doubles the frequency corresponding to the peak shear stress. For shear-thinning liquids, the velocity profiles are predicted to contain inflection points suggesting that the flow induced in the liquid is vulnerable to hydrodynamic instability. A parameter study reveals that the time-constant in the Carreau model strongly controls the flow kinematics and dynamics during bubble oscillations. The conclusion is that blood shear-thinning behavior should be considered in cases where bubbles are used as contrast agents.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"347 ","pages":"Article 105514"},"PeriodicalIF":2.8,"publicationDate":"2025-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145419946","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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号