Viscoelastic fluids are non-Newtonian fluids that exhibit both "viscous" and "elastic" characteristics in virtue of mechanisms to store energy and produce entropy. Usually the energy storage properties of such fluids are modelled using the same concepts as in the classical theory of nonlinear solids. Recently new models for elastic solids have been successfully developed by appealing to implicit constitutive relations, and these new models offer a different perspective to the old topic of elastic response of materials. In particular, a sub-class of implicit constitutive relations, namely relations wherein the left Cauchy-Green tensor is expressed as a function of stress is of interest. We show how to use this new perspective it the development of mathematical models for viscoelastic fluids, and we provide a discussion of the thermodynamic underpinnings of such models. We focus on the use of Gibbs free energy instead of the Helmholtz free energy, and using the standard Giesekus/Oldroyd-B models, we show how the alternative approach works in the case of well-known models. The proposed approach is straightforward to generalise to more complex setting wherein the classical approach might be impractical of even inapplicable.
Lagrangian dynamics unveil polymer conformation in viscoelastic flows
Tufts University（塔夫茨大学）；Institute for Mechanobiology, Department of Bioengineering, College of Engineering, Northeastern University（东北大学生物工程学院机制生物学研究所）；Department of Mechanical Science and Engineering, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校机械科学与工程系）；Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania（宾夕法尼亚大学机械工程和应用力学系）
Wall-induced translation of a rotating particle in viscoelastic fluid
剪切变稀和粘弹性是生物流体中广泛存在的两种非牛顿流体性质。在这项研究中，我们发现，在壁面附近的旋转颗粒的平移运动首先加速，然后随着流体粘弹性的增强而减慢，这与剪切稀化流体中报道的行为不同（Chen et al. J. Fluid Mech.2021，927）。本文采用纳维-斯托克斯方程结合Oldrophil-B本构模型进行数值模拟。这一工作将有助于全面理解复杂流体中旋转球在近壁面处的运动。
A semi-analytical solution for the lubrication force between two spheres approaching in viscoelastic fluids described by the Oldroyd-B model under small Deborah numbers
Learning constitutive models and rheology from partial flow measurements
John A. Paulson School of Engineering and Applied Sciences, Harvard University（哈佛大学约翰·A·保尔森工程与应用科学学院）；School of Engineering, Brown University（布朗大学工程学院）；Research and Development Center, Saudi Aramco（沙特阿美研发中心）；Department of Physics, Harvard University（哈佛大学物理系）
Fully-implicit log-conformation formulation of constitutive laws
RWTH Aachen University（亚琛工业大学）；Chair for Computational Analysis of Technical Systems (CATS)（技术系统计算分析讲席）；Center for Computational Engineering Science (CCES)（计算工程科学中心）
