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The viscoelastic dynamic model for profile evolution of photoresist formed during thermal reflow 热回流过程中光刻胶轮廓演变的粘弹性动力学模型
IF 2.7 2区 工程技术 Q2 MECHANICS Pub Date : 2025-05-19 DOI: 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 %.
为了用热回流法研究光刻胶微观结构(如微透镜)的轮廓形成,基于运动方程、连续性方程和薄膜假设建立了粘弹性动力学模型。该模型考虑了粘弹性、表面张力以及交联效应对聚合物熔体剖面演化的影响,采用Oldroyd-B模型描述聚合物熔体的粘弹性本构关系。由于本文建立的粘弹性动力学模型是一个关于聚合物熔体轮廓高度函数的微分方程,因此通过数值耦合膜厚方程和Oldroyd-B本构方程的解,可以在形状演化过程中自然地得到聚合物熔体的自由表面轮廓。与求解粘弹性流体力学的高度非线性方程相比,采用该方程可提高自由面剖面数值模拟的计算效率。利用该模型分析了烘烤时间、烘烤温度、交联效应等关键参数对型材形状演变的影响,并通过分配不同的Weissenberg数对材料进行了比较。此外,仿真预测的最终廓形与实验结果的验证实验最大相对误差小于10%。
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引用次数: 0
Extensional properties of dilute polymer solutions with different molecular weights measured using piezo-driven extensional rheometry 用压电驱动拉伸流变法测量了不同分子量的稀聚合物溶液的拉伸特性
IF 2.7 2区 工程技术 Q2 MECHANICS Pub Date : 2025-05-14 DOI: 10.1016/j.jnnfm.2025.105422
T. Matsuda , M. Muto , S. Tamano
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 cmin, 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).
使用高速摄像机拍摄和分析了填充了稀释聚合物溶液(PEO,聚乙烯氧化物)的按需滴注(DOD)头喷射出的细丝。在较低的PEO浓度下,灯丝的衰变速度更快,在极低的浓度下几乎完全相同。拉伸弛豫时间随PEO浓度的减小呈幂律规律减小,在临界浓度cmin附近接近于一个几乎恒定的值,接近理论极限。经重叠浓度归一化的PEO浓度与经Zimm弛豫时间归一化的弛豫时间在对数图上均呈线性关系,且与分子量无关。压电驱动拉伸流变仪的幂律指数与之前的研究报告类似,例如使用液体滴注(LD)法、毛细管破裂拉伸流变仪(CaBER)和瑞利-欧内乔治喷射拉伸流变仪(ROJER)。
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引用次数: 0
Modelling of the pressure-driven tube flow of the shear-thinning fluids with solid particles 含固体颗粒剪切稀化流体的压力驱动管流模型
IF 2.7 2区 工程技术 Q2 MECHANICS Pub Date : 2025-05-13 DOI: 10.1016/j.jnnfm.2025.105430
A.A. Gavrilov , A.V. Shebelev , A.V. Minakov
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.
在悬浮液平衡模型的基础上,建立了剪切减薄流体悬浮液流动的连续体模型。将悬架模型推广到服从Herschel-Bulkley定律的剪切-变薄屈服应力流体,需要考虑剪切速率放大效应和颗粒阻力的修正。此外,该模型利用相对速度的输运方程考虑了惯性和非定常粒子效应。为了验证所提出的模型,数值模拟了具有中性浮力和重颗粒的悬浮液在圆形管道中的压力驱动层流。结果表明,在一定条件下,所建立的模型能较好地描述含固体颗粒的剪切变薄屈服应力流体的各种流动形式,从含固定沉积层的非均质流动到含悬浮颗粒的流动。考虑了重颗粒悬浮流的一个重要问题——颗粒输运效率的评估。考虑了流的一些整体特性的依赖关系。
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引用次数: 0
Large amplitude oscillatory extension (LAOE) of dilute polymer solutions 稀聚合物溶液的大振幅振荡扩展(LAOE)
IF 2.7 2区 工程技术 Q2 MECHANICS Pub Date : 2025-05-12 DOI: 10.1016/j.jnnfm.2025.105421
Steffen M. Recktenwald , Thomas P. John , Amy Q. Shen , Robert J. Poole , Cláudio P. Fonte , Simon J. Haward
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.
本文提出了一个用于研究复杂流体非线性材料特性的大振幅振荡扩展(LAOE)实验框架。使用微流体优化形状的交叉槽拉伸流变仪,我们产生近似均匀的平面拉伸流,由可编程注射泵驱动,以振荡或脉冲正弦模式运行。采用微颗粒图像测速法和同步压降法分析了随时间变化的流场和弹性应力响应。对于牛顿流体,在很宽的振荡幅度和频率范围内,可以观察到施加应变率与压降之间的线性关系。相比之下,稀聚合物溶液在LAOE循环过程中表现出明显的偏差,在拉伸和压缩轴上存在超压降和平均应变率之间的分歧。通过跨越广泛的Weissenberg和Deborah数,我们确定了振荡扩展下唯一的Lissajous曲线和非线性开始的临界条件。假设均匀流动的数值模拟支持实验结果,验证了我们的微流体方法的鲁棒性。这项研究证明了振荡拉伸流在探测软材料的非线性流变行为方面的效用,为其在非线性流动条件下的拉伸特性提供了定量的见解。
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引用次数: 0
Experimental investigation on drag reduction in turbulent pipe flow with polymer injection 注入聚合物对湍流管流减阻的实验研究
IF 2.7 2区 工程技术 Q2 MECHANICS Pub Date : 2025-05-09 DOI: 10.1016/j.jnnfm.2025.105434
Pengfei Shi , Haibao Hu , Jun Wen , Hailang Sun , Luo Xie
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 K in the flat plate boundary layer flow with polymer injection, the normalized polymer flux Kp 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 Kp-scaling laws indicate that DR firstly grows linearly, and then saturates or even declines with increasing log10 Kp, similar to the observed DR variation of the plate boundary layer flow with polymer injection. The DR vs Kp 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.
通过实验研究了聚氧乙烯溶液的减阻特性及其对注入聚合物的管内湍流流动的影响。该研究系统地考察了雷诺数、注入角(7个角)、分子量(7个分子量)和流向发展对减阻的影响。与注入聚合物的平板边界层流动中无量纲聚合物通量K相似,定义适用于管道的归一化聚合物通量Kp(即注入聚合物与主流的相对质量比),进一步压缩实验数据。Kp标度规律表明,随着log10 Kp的增加,DR先呈线性增长,然后趋于饱和甚至下降,这与观察到的注入聚合物后板边界层流动DR的变化规律相似。DR / Kp关系可以为优化聚合物注入在管道流动中的使用提供指导。减阻量随分子量的变化规律符合s型曲线,可为优化分子量在聚合物减阻中的应用提供指导。当雷诺数为15,952 ~ 79,761时,减阻变化先增大后减小;存在达到最佳减阻效果的临界雷诺数。减阻率随注入角度和流向距离的变化受注入液有效浓度和注入液平流的影响。较小的喷射角并不能带来更显著的减阻效果。同时,在一定条件下,反流喷射比顺流喷射表现出更好的减阻效果,这主要是受更合适的混合速率的影响。
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引用次数: 0
Equilibrium position and rotational behaviours of spheroid in an inertial rectangular microchannel flow of Oldroyd-B viscoelastic fluid Oldroyd-B粘弹性流体惯性矩形微通道中球体的平衡位置和旋转行为
IF 2.7 2区 工程技术 Q2 MECHANICS Pub Date : 2025-05-05 DOI: 10.1016/j.jnnfm.2025.105431
Xiao Hu , Jianzhong Lin , Zhaosheng Yu , Zhaowu Lin , Jingyu Cui , Yan Xia
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.
采用直接强迫/虚拟域方法研究了Oldroyd-B粘弹性流体惯性矩形微通道中球体的平衡位置和旋转行为。结果表明,在惯性矩形通道中,长形(扁圆)球体的弹惯性迁移存在5种平衡位置和4种旋转行为。随着弹性数的减小,球体逐渐转变为边角(CO)、通道中心线(CC)、近边角(NCO)、近通道中心(NCC)和长壁等分线(BLW)平衡位置,NCO和NCC平衡位置是本文新发现的。当流体弹性较大时,只有大球体显示异常的离中心NCC平衡位置。随着流体惯量的增加,颗粒附近的诱导横向迁移速度增强,诱导流线将所有颗粒推离CC平衡位置。球形颗粒表现出最高的诱导速度,其次是扁圆球体,而长条形球体诱导的横向迁移速度最低,并且始终表现出离通道中心最近的距离。颗粒粒径越小,流体弹性越大,颗粒越靠近通道中心。这些结果对设计高分离效率的微流控芯片具有一定的指导意义。
{"title":"Equilibrium position and rotational behaviours of spheroid in an inertial rectangular microchannel flow of Oldroyd-B viscoelastic fluid","authors":"Xiao Hu ,&nbsp;Jianzhong Lin ,&nbsp;Zhaosheng Yu ,&nbsp;Zhaowu Lin ,&nbsp;Jingyu Cui ,&nbsp;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}
引用次数: 0
Control of viscoplastic fluid dynamics in superhydrophobic channels with asymmetric groove configurations 非对称槽型超疏水通道粘塑性流体动力学控制
IF 2.7 2区 工程技术 Q2 MECHANICS Pub Date : 2025-04-21 DOI: 10.1016/j.jnnfm.2025.105420
A. Joulaei , H. Rahmani , S.M. Taghavi
We study the plane Poiseuille flow of viscoplastic fluids in channels with asymmetric superhydrophobic (SH) walls featuring transverse groove configurations in the thin channel limit. We use OpenFOAM simulations and the Papanastasiou regularization method to approximate the Bingham model. Focusing on variations in the upper SH wall’s characteristics, we explore the effects of slip number (b2), groove periodicity length (2), slip area fraction (φ2), and Bingham number (B) on flow dynamics, flow metrics and unyielded center plug morphology. We find that increasing b2, φ2, and 2 enhances slip velocity on the upper SH wall and reduces the normalized plug area (A/A0) up to φ2=0.5, while higher B amplifies flow asymmetry, shifting and breaking center plugs. By introducing the concept of slippery equivalent systems, we demonstrate that varying groove configurations can yield identical effective slip lengths (χT) with distinct plug morphologies, enabling precise control of viscoplastic fluid dynamics. We derive a simplified model to predict χT and A/A0, identifying a critical threshold at A/A00.68 for regime transitions between unbroken (Regime I) and broken (Regime II) center plugs, leading to a six-dimensional manifold equation for classifying these regimes across parameter space.
本文研究了粘塑性流体在具有横向沟槽结构的非对称超疏水(SH)壁面通道中的平面泊泽维尔流动。我们使用OpenFOAM模拟和Papanastasiou正则化方法来近似Bingham模型。针对上斜壁特征的变化,我们探讨了滑移数(b2)、槽周期长度(l2)、滑移面积分数(φ2)和Bingham数(B)对流动动力学、流动指标和未屈服中心塞形态的影响。结果表明,增大b2、φ2和φ2可以提高上斜壁的滑移速度,减小标准化塞面积(A/A0) (φ2=0.5),而增大B则会放大流动不对称、中心塞的移位和破裂。通过引入滑等效系统的概念,我们证明了不同的沟槽配置可以在不同的桥塞形态下产生相同的有效滑移长度(χT),从而实现粘塑性流体动力学的精确控制。我们推导了一个简化模型来预测χT和a /A0,确定了在a /A0≈0.68处的临界阈值,用于未破坏(状态I)和破坏(状态II)中心塞之间的状态转换,从而得到一个用于跨参数空间对这些状态进行分类的六维流形方程。
{"title":"Control of viscoplastic fluid dynamics in superhydrophobic channels with asymmetric groove configurations","authors":"A. Joulaei ,&nbsp;H. Rahmani ,&nbsp;S.M. Taghavi","doi":"10.1016/j.jnnfm.2025.105420","DOIUrl":"10.1016/j.jnnfm.2025.105420","url":null,"abstract":"<div><div>We study the plane Poiseuille flow of viscoplastic fluids in channels with asymmetric superhydrophobic (SH) walls featuring transverse groove configurations in the thin channel limit. We use OpenFOAM simulations and the Papanastasiou regularization method to approximate the Bingham model. Focusing on variations in the upper SH wall’s characteristics, we explore the effects of slip number (<span><math><msub><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>), groove periodicity length (<span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>), slip area fraction (<span><math><msub><mrow><mi>φ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>), and Bingham number (<span><math><mi>B</mi></math></span>) on flow dynamics, flow metrics and unyielded center plug morphology. We find that increasing <span><math><msub><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, <span><math><msub><mrow><mi>φ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, and <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> enhances slip velocity on the upper SH wall and reduces the normalized plug area (<span><math><mrow><mi>A</mi><mo>/</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></math></span>) up to <span><math><mrow><msub><mrow><mi>φ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></math></span>, while higher <span><math><mi>B</mi></math></span> amplifies flow asymmetry, shifting and breaking center plugs. By introducing the concept of <em>slippery equivalent systems</em>, we demonstrate that varying groove configurations can yield identical effective slip lengths (<span><math><msub><mrow><mi>χ</mi></mrow><mrow><mi>T</mi></mrow></msub></math></span>) with distinct plug morphologies, enabling precise control of viscoplastic fluid dynamics. We derive a simplified model to predict <span><math><msub><mrow><mi>χ</mi></mrow><mrow><mi>T</mi></mrow></msub></math></span> and <span><math><mrow><mi>A</mi><mo>/</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></math></span>, identifying a critical threshold at <span><math><mrow><mi>A</mi><mo>/</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>≈</mo><mn>0</mn><mo>.</mo><mn>68</mn></mrow></math></span> for regime transitions between unbroken (Regime I) and broken (Regime II) center plugs, leading to a six-dimensional manifold equation for classifying these regimes across parameter space.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"341 ","pages":"Article 105420"},"PeriodicalIF":2.7,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143869095","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}
引用次数: 0
Flow of a two-dimensional liquid foam: Impact of surfactant type and boundary conditions 二维液体泡沫的流动:表面活性剂类型和边界条件的影响
IF 2.7 2区 工程技术 Q2 MECHANICS Pub Date : 2025-04-10 DOI: 10.1016/j.jnnfm.2025.105417
Farshad Nazari , Andrei Potanin , Hadi Mohammadigoushki
In this study, we experimentally investigate the rheological and flow behavior of two-dimensional (2D) monodisperse aqueous foams, sheared between parallel plates using a custom-made rheo-optical apparatus with smooth and roughened walls. The foams were prepared using two commercially available detergents — Foam 1 and Foam 2 — while maintaining similar bubble sizes and liquid fractions. The linear viscoelastic results reveal that the Foam 1 consistently exhibits higher elastic and loss moduli than the Foam 2, regardless of boundary conditions, with roughened walls further enhancing these moduli in both foams. Additionally, the Foam 1 shows a lower viscoelastic relaxation frequency compared to the Foam 2, indicating a less mobile interface for the Foam 1. In the non-linear regime, significant differences were observed. Under smooth boundary conditions, Foam 2 exhibits yield stress behavior, whereas Foam 1 does not, despite having higher viscous stresses. The viscous stress in the Foam 1 scales with the capillary number as τw Ca0.5, while for the Foam 2, the scaling depends on the boundary conditions: τw Ca0.85 for smooth walls and τw Ca0.65 for roughened walls. These variations in rheological behavior are attributed to differences in surfactant chemistry, leading to different interface mobilities, with the Foam 1 having a less mobile interface compared to the Foam 2.
在这项研究中,我们通过实验研究了二维单分散水泡沫在平行板之间剪切的流变学和流动行为,使用了定制的具有光滑和粗糙壁的流变光学装置。泡沫是用两种市售洗涤剂——Foam 1和Foam 2制备的,同时保持相似的气泡大小和液体分数。线性粘弹性结果表明,无论边界条件如何,泡沫1始终表现出比泡沫2更高的弹性和损失模量,粗糙的壁进一步提高了两种泡沫的弹性和损失模量。此外,与Foam 2相比,Foam 1显示出较低的粘弹性松弛频率,这表明Foam 1的移动界面较少。在非线性状态下,观察到显著的差异。在光滑边界条件下,泡沫2表现出屈服应力行为,而泡沫1尽管具有更高的粘性应力,但没有屈服应力行为。泡沫1的黏性应力以毛细数τw∝Ca0.5为尺度,而泡沫2的黏性应力取决于边界条件:光滑壁面τw∝Ca0.85,粗糙壁面τw∝Ca0.65。这些流变行为的变化归因于表面活性剂化学性质的差异,导致不同的界面迁移率,与泡沫2相比,泡沫1具有更少的移动界面。
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引用次数: 0
Unusual rheological behavior of a moderately entangled telechelic polymer and hollow glass microsphere suspension via hydrogen bonding interactions 适度纠缠的远旋聚合物和中空玻璃微球悬浮液通过氢键相互作用的不寻常流变行为
IF 2.7 2区 工程技术 Q2 MECHANICS Pub Date : 2025-04-08 DOI: 10.1016/j.jnnfm.2025.105419
Praveen Sreenivasan , Srikanth Billa , Sangram Kesari Rath , Debdatta Ratna , Santanu Chattopadhyay
The understanding of rheological behavior of non-Brownian hard sphere suspensions is of importance from both the fundamental and applied perspectives. This is owing to their ubiquitous use in industry for many applications. However, most of the studies reported in literature pertain to non-colloidal hard sphere suspensions in a Newtonian matrix. In the present work, we report the rheological response of hollow glass microspheres (HGMs) suspended in a moderately entangled telechelic polymer of hydroxyl terminated polybutadiene (HTPB) across a wide concentration range i.e., volume fraction, ɸ varying from 0.07 to 0.6. Steady state and small amplitude oscillatory rheology (SAOR) measurements of the suspensions revealed a significant departure of the rheological response from that of non-Brownian hard sphere suspensions. The salient findings of the study are (a) pronounced shear thinning (b) increased storage and loss moduli with increased HGM content (c) low frequency storage moduli plateau across concentrations (d) percolation at ɸ =0.49–0.51 of HGM (e) significant difference in the high frequency dynamic modulus between HTPB and suspensions at ɸ > 0.5. Some of these rheological features resemble that of colloidal or Brownian suspensions and are suggestive of formation of network or gel-like structure. We invoke the role of HTPB-HGM interaction (FTIR spectroscopy), morphology of the suspensions (optical microscopy), plausible immobilization of telechelic chains on surface of HGM, entangled state of the telechelic as the mechanistic origins of the observed unusual rheological behavior of the studied suspensions. We posit that the present study is an important addition to experimental investigations in the field of hard sphere dispersions.
了解非布朗硬球悬浮液的流变行为,从基础和应用的角度都具有重要意义。这是由于它们在工业中普遍用于许多应用程序。然而,文献中报道的大多数研究都涉及牛顿矩阵中的非胶体硬球悬浮液。在本研究中,我们报道了悬浮在端羟基聚丁二烯(HTPB)的中等纠缠远螺旋聚合物中的中空玻璃微球(HGMs)在较宽的浓度范围内的流变响应,即体积分数,从0.07到0.6不等。悬浮液的稳态和小振幅振荡流变(SAOR)测量表明,流变响应与非布朗硬球悬浮液的流变响应有很大的不同。研究发现:(a)显著的剪切变薄(b)随着HGM含量的增加,储水量和损失模量增加(c)低频储水量模量跨越浓度平台(d)在HGM的h = 0.49-0.51时的渗流(e)在h >时HTPB与悬浮液的高频动态模量存在显著差异;0.5. 其中一些流变学特征类似于胶体或布朗悬浮液,表明形成了网状或凝胶状结构。我们将HTPB-HGM相互作用的作用(FTIR光谱)、悬浮液的形貌(光学显微镜)、HGM表面的远旋链的合理固定、远旋链的纠缠态作为所研究悬浮液观察到的不寻常流变行为的机制起源。我们认为本研究对硬球色散领域的实验研究是一个重要的补充。
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引用次数: 0
Simulation of the extensional deformation of a drop with an elastoviscoplastic interface 弹粘塑性界面液滴拉伸变形的模拟
IF 2.7 2区 工程技术 Q2 MECHANICS Pub Date : 2025-04-01 DOI: 10.1016/j.jnnfm.2025.105408
M.A. Carrozza , M. Hütter , L.G.B. Bremer , P.D. Anderson , M.A. Hulsen
A numerical implementation of two-phase flows of Newtonian fluids with a non-linear viscoelastic interface is validated and applied to the case of uniaxial extension of a drop in a matrix fluid. Second-order convergence in space and time is obtained with a Lagrangian-based interface tracking finite element method. The flow problem is analysed using dimensionless groups based on the relative magnitudes of the viscoelastic interfacial extra stress, the interfacial tension and the viscous stress of the bulk fluids. After fitting the intrinsic viscoelastic stress–strain behaviour of interfaces in shear to experimental results from the literature, the influence of interfacial rheology on the drop shape and interfacial stress is investigated. The drop shape is not significantly influenced by the viscoelastic properties of the interface if the interfacial viscoelastic stress, interfacial tension and bulk viscous stress are of the same order of magnitude. However, the interface develops distinct stress profiles for varying interfacial viscoelastic properties. For relatively large viscoelastic interface stress compared to interfacial tension and bulk viscous stress, simulations become unstable. Eventually, the interfacial viscoelastic stress exceeds the interfacial tension and bulk viscous stress, and possibly buckling of the interface occurs, caused by compressive stresses at the drop tip.
验证了具有非线性粘弹性界面的牛顿流体两相流动的数值实现,并将其应用于液滴在基质流体中单轴扩展的情况。利用基于拉格朗日的界面跟踪有限元方法,得到了空间和时间上的二阶收敛性。根据粘弹性界面额外应力、界面张力和黏性应力的相对大小,采用无量纲群对流动问题进行了分析。将剪切界面的粘弹性应力-应变特性与文献实验结果拟合后,研究了界面流变对液滴形状和界面应力的影响。当界面粘弹性应力、界面张力和体粘应力处于同一数量级时,液滴形态不受界面粘弹性特性的显著影响。然而,由于界面粘弹性的不同,界面产生了不同的应力分布。对于相对较大的粘弹性界面应力,与界面张力和体粘性应力相比,模拟变得不稳定。最终,界面粘弹性应力超过界面张力和体粘性应力,并可能发生界面屈曲,这是由水滴尖端的压应力引起的。
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Journal of Non-Newtonian Fluid Mechanics
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