Anisotropic Oldroyd-type models for non-colloidal suspensions of viscoelastic particles in Newtonian and yield-stress fluids via homogenization

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