发表机构
University of Wisconsin-Madison; Indian Institute of Science, Bangalore; University of California Santa Barbara（威斯康星大学麦迪逊分校; 印度科学研究所班加罗尔分院; 加州大学圣塔芭芭拉分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出一种结合速度与微观结构测量及连续介质力学的方法，分两步揭示流动复杂流体的应力张量，并通过聚合物溶液模拟数据验证了方法的有效性与鲁棒性。
AI 中文摘要
流动的复杂流体（如聚合物、表面活性剂和/或胶体颗粒的溶液）中的应力是材料的基本动态性质。它反映了流体在变形下微观结构的演化，并决定了流体的运动。虽然可以通过测速法获得流动的空间分辨测量，通过散射等方法获得微观结构的空间分辨测量，但这两者中的任何一个都无法单独唯一地确定应力。特别是，由于应力张量与微观结构施加在流体上的净力之间的关系具有简并性，应力张量无法直接观测。我们表明，将速度与微观结构测量与连续介质力学原理相结合，可以打破这种简并性，揭示应力张量。该方法分为两个阶段。第一阶段，利用速度信息以及动量和质量守恒方程，通过数据同化框架推断微观结构施加在流体上的力密度。第二阶段，求解力密度与应力之间的关系方程。该方程具有非平凡的零空间，引入了一个齐次解，其结构必须被确定才能唯一地确定应力。我们通过使用微观结构数据和微观结构与应力之间的一般模型来实现这一点，该模型的参数以及零空间解通过求解最小二乘问题来确定。该方法使用流动聚合物溶液模拟产生的合成速度和微观结构数据进行了说明，证明了其有效性和鲁棒性。
英文摘要
The stress in a flowing complex fluid such as a solution of polymers, surfactants and/or colloidal particles is a fundamental dynamic property of the material. It reflects the evolution of the fluid microstructure under deformation and determines the motion of the fluid. While spatially resolved measurements of flow (via velocimetry) and microstructure (e.g.~via scattering) can be made, neither of these individually can uniquely determine the stress. In particular, due to the degenerate nature of the relationship between the stress tensor and the net force exerted by the microstructure on the fluid, the stress tensor is hidden from direct observation. We show that integrating velocity and microstructure measurements with principles of continuum mechanics can break this degeneracy, unveiling the stress tensor. The approach has two stages. In the first, velocity information is used along with the momentum and mass conservation equations to infer the force density exerted by the microstructure on the fluid using a data assimilation framework. In the second, the equation relating force density to stress is solved. This equation has a nontrivial nullspace, introducing a homogeneous solution whose structure must be found to uniquely determine the stress. We do so by using microstructural data and a general model between microstructure and stress, the parameters of which are determined, along with the nullspace solution, by solving a least-squares problem. The approach is illustrated using synthetic velocity and microstructural data from simulation of a flowing polymer solution, demonstrating its validity and robustness.
