Gianluca Santesarti , Michele Marino , Francesco Viola , Roberto Verzicco , Giuseppe Vairo
{"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}
Qiaoyan Ye , Wolfgang Niemeier , Oliver Tiedje , Bo Shen
{"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}
{"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}
Tongsheng Wang , Erik Steur , Tess Homan , Patrick R. Onck , Jaap M.J. den Toonder , Ye Wang
{"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}
Xi Lin , Qi Li , Yufan Yang , Yan Xing , XiaoHui Lin , Chibin Zhang , Qing Chai
{"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}
{"title":"Extensional properties of dilute polymer solutions with different molecular weights measured using piezo-driven extensional rheometry","authors":"T. Matsuda , M. Muto , S. Tamano","doi":"10.1016/j.jnnfm.2025.105422","DOIUrl":"10.1016/j.jnnfm.2025.105422","url":null,"abstract":"<div><div>Filaments ejected from a drop-on-demand (DOD) head filled with a dilute polymer solution (PEO, polyethylene oxide) were photographed and analyzed using a high-speed camera. The filament decay was faster at lower PEO concentrations and became nearly identical at extremely low concentrations. The extensional relaxation time decreased with as the PEO concentration decreased following the power law, and approached an almost constant value near the critical concentration <span><math><msub><mrow><mi>c</mi></mrow><mrow><mi>min</mi></mrow></msub></math></span>, which is close to the theoretical limit. The relationship between the PEO concentration normalized by the overlapping concentration and the relaxation time normalized by the Zimm relaxation time was linear in both logarithmic graphs and independent of molecular weight. The power-law exponent in piezo-driven extensional rheometry is similar to that reported in previous studies, such as those using the liquid dripping (LD) method, capillary breakup extensional rheometry (CaBER), and Rayleigh–Ohnesorge jetting extensional rheometry (ROJER).</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"341 ","pages":"Article 105422"},"PeriodicalIF":2.7,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144099164","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":"Modelling of the pressure-driven tube flow of the shear-thinning fluids with solid particles","authors":"A.A. Gavrilov , A.V. Shebelev , A.V. Minakov","doi":"10.1016/j.jnnfm.2025.105430","DOIUrl":"10.1016/j.jnnfm.2025.105430","url":null,"abstract":"<div><div>A continuum model of shear-thinning fluid suspension flow based on suspension balance model is developed. The generalization of the suspension model to the shear-thinning yield stress fluids, obeying the Herschel-Bulkley law, requires taking into account the shear rate amplification effect and modification of the particle drag force. Additionally, the model includes inertial and unsteady particle effects by using the transport equation for relative velocity. To validate the proposed model, pressure-driven laminar flows of suspensions with neutrally buoyant and heavy particles in circular pipes are numerically simulated. The results show that, at certain conditions, the developed model can adequately describe various flow regimes of shear-thinning yield stress fluids with solid particles, from heterogeneous flows with a stationary sediment layer to flows with suspended particles. An important issue for suspension flows with heavy particles is considered - assessment of the particle transport efficiency. Dependencies of some integral characteristics of the flow are considered.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"341 ","pages":"Article 105430"},"PeriodicalIF":2.7,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144099248","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}
Steffen M. Recktenwald , Thomas P. John , Amy Q. Shen , Robert J. Poole , Cláudio P. Fonte , Simon J. Haward
{"title":"Large amplitude oscillatory extension (LAOE) of dilute polymer solutions","authors":"Steffen M. Recktenwald , Thomas P. John , Amy Q. Shen , Robert J. Poole , Cláudio P. Fonte , Simon J. Haward","doi":"10.1016/j.jnnfm.2025.105421","DOIUrl":"10.1016/j.jnnfm.2025.105421","url":null,"abstract":"<div><div>This study presents an experimental framework for large amplitude oscillatory extension (LAOE) to investigate nonlinear material properties of complex fluids. Using a microfluidic optimized shape cross-slot extensional rheometer, we generate approximately homogeneous planar extensional flows driven by programmable syringe pumps operating in oscillatory or pulsatile sinusoidal modes. Micro-particle image velocimetry and simultaneous pressure drop measurements are employed to analyze the time-dependent flow field and elastic stress response. For Newtonian fluids, a linear relationship between the applied strain rate and pressure drop is observed across a wide range of oscillation amplitudes and frequencies. In contrast, dilute polymer solutions exhibit significant deviations, with excess pressure drops and divergence between average strain rates along extension and compression axes during the LAOE cycle. By spanning a broad range of Weissenberg and Deborah numbers, we identify unique Lissajous curves and critical conditions for the onset of nonlinearities under oscillatory extension. Numerical simulations, assuming homogeneous flow, underpin the experimental findings, validating the robustness of our microfluidic approach. This study demonstrates the utility of oscillatory extensional flows for probing the nonlinear rheological behavior of soft materials, offering quantitative insights into their extensional properties under nonlinear flow conditions.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"342 ","pages":"Article 105421"},"PeriodicalIF":2.7,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144114847","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}
Pengfei Shi , Haibao Hu , Jun Wen , Hailang Sun , Luo Xie
{"title":"Experimental investigation on drag reduction in turbulent pipe flow with polymer injection","authors":"Pengfei Shi , Haibao Hu , Jun Wen , Hailang Sun , Luo Xie","doi":"10.1016/j.jnnfm.2025.105434","DOIUrl":"10.1016/j.jnnfm.2025.105434","url":null,"abstract":"<div><div>An experimental investigation is conducted to characterize the drag reduction of Polyethylene Oxide solutions and its influencing on turbulent pipe flow with polymer injection. The study systematically examines the effects of Reynolds number, injection angle (seven angles), molecular weight (seven molecular weights), and streamwise direction development on drag reduction. Similar to the dimensionless polymer flux <em>K</em> in the flat plate boundary layer flow with polymer injection, the normalized polymer flux <em>K</em><sub><em>p</em></sub> applicable to the pipe (i.e., the relative mass ratio between the injecting polymer and the main flow) is defined to further collapse experimental data. The <em>K</em><sub><em>p</em></sub>-scaling laws indicate that DR firstly grows linearly, and then saturates or even declines with increasing log<sub>10</sub> <em>K</em><sub><em>p</em></sub>, similar to the observed DR variation of the plate boundary layer flow with polymer injection. The DR vs <em>K</em><sub><em>p</em></sub> relationship could provide guidance to optimize the use of polymer injection for the pipeline flow. Notably, the variation law of drag reduction with molecular weight conforms to S-shaped curve, which can provide guidance to optimize the use of molecular weight in polymers drag reduction. The change in drag reduction with Reynolds number varying from 15,952 to 79,761 initially increases and then decreases; there exists a critical Reynolds number for achieving optimal drag reduction effect. The variation of drag reduction rate with injection angle and streamwise direction distance is influenced by both effective concentration and advection of the injected solution. Smaller injection angle does not bring more significant drag reduction effect. Meanwhile, the counter-stream injection exhibits a superior drag reduction effect compared to streamwise injection under certain conditions, primarily due to the influence of more suitable mixing rate.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"341 ","pages":"Article 105434"},"PeriodicalIF":2.7,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144072381","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}
Xiao Hu , Jianzhong Lin , Zhaosheng Yu , Zhaowu Lin , Jingyu Cui , Yan Xia
{"title":"Equilibrium position and rotational behaviours of spheroid in an inertial rectangular microchannel flow of Oldroyd-B viscoelastic fluid","authors":"Xiao Hu , Jianzhong Lin , Zhaosheng Yu , Zhaowu Lin , Jingyu Cui , Yan Xia","doi":"10.1016/j.jnnfm.2025.105431","DOIUrl":"10.1016/j.jnnfm.2025.105431","url":null,"abstract":"<div><div>Equilibrium position and rotational behaviours of spheroid in an inertial rectangular microchannel flow of Oldroyd-B viscoelastic fluid is studied by the direct forcing/fictitious domain method. The results show that there are five kinds of equilibrium positions and four (three) kinds of rotational behaviours for the elasto-inertial migration of prolate (oblate) spheroids in an inertial rectangular channel flow. The spheroids gradually change to the corner (CO), channel centreline (CC), near corner (NCO), near channel centre (NCC) and bisector of the long wall (BLW) equilibrium positions as the elastic number decreases, the NCO and NCC equilibrium positions are newly found in the present works. When the fluid elasticity is large, only the large sphere displays the anomalous off-centreline NCC equilibrium position. With increasing the fluid inertia, the induced lateral migration velocity near the particle is enhanced, and the induced streamlines push all particles away from the CC equilibrium position. Spherical particles exhibit the highest induced velocity, then followed by the oblate spheroids, while prolate spheroids induce the lowest lateral migration velocity and consistently exhibit the closest distance to the channel centre. The particles are closer to the channel centre with decreasing the particle size, and with increasing the fluid elasticity. Those results are useful for designing a microfluidic chip with high separation efficiency.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"341 ","pages":"Article 105431"},"PeriodicalIF":2.7,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143923750","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}