This paper makes use of homogenization to generate a fairly general class of rheological models for non-colloidal suspensions of particles undergoing finite deformations and rotations under Stokes flow conditions. The particles can be nonlinear viscoelastic, or elasto-viscoplastic, while the suspending fluid can be Newtonian or viscoplastic. The microstructure is described by two microstructural ellipsoids, which are allowed to evolve with the flow, characterizing the shape and orientation of the inclusions and the angular dependence of their distribution in space. The models account for particle interactions through the two-point correlation function for the particle centers, in a way that reproduces exactly classical and more recent estimates for dilute suspensions. While special cases of the models have been considered in earlier publications, novel features of this work include the possibility of multiple inclusion families, physically motivated evolutions laws for the particle distributions and more general rheological behaviors for the matrix and inclusions. The resulting models can be viewed as anisotropic generalizations of Oldroyd’s invariant models accounting for statistical measures of the microstructure and their evolution.

本文利用均质化为在斯托克斯流动条件下经历有限变形和旋转的颗粒的非胶体悬浮液生成一类相当通用的流变模型。颗粒可以是非线性粘弹性或弹粘塑性，而悬浮流体可以是牛顿流体或粘塑性。微观结构由两个微观结构椭球描述，它们可以随着流动而演变，表征夹杂物的形状和取向以及它们在空间中分布的角度依赖性。这些模型通过粒子中心的两点相关函数来解释粒子相互作用，其方式精确地再现了对稀悬浮液的经典和更新估计。虽然在早期的出版物中已经考虑了模型的特殊情况，这项工作的新特点包括多个夹杂物家族的可能性、粒子分布的物理动机演化规律以及基质和夹杂物的更一般的流变行为。由此产生的模型可以被视为Oldroyd 不变模型的各向异性概括说明了微观结构及其演化的统计测量。