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

Abstract

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. • Rheological models for suspensions of deformable particles in yield stress fluids. • Models are based on homogenization techniques for linear and nonlinear media. • The particles can be nonlinear viscoelastic or viscoplastic and the fluid Newtonian or viscoplastic. • Two ellipsoids characterize the evolution of the average particle shape and distribution. • The resulting models can be viewed as anisotropic generalizations of Oldroyd’s invariant models.