A theoretical framework for granular suspensions in a steady simple shear flow

We focus our attention on granular suspensions made up of noncolloidal spherical particles within a Newtonian fluid. The main objective of this paper is to provide a general framework for the formulation of the bulk stress tensor. The bulk stress within granular suspensions is mainly generated at the particle level by strong interactions between particles, such as friction, collision, and lubricated contact. The existence of a few local mechanisms is a major cause of behavior complexity at the macroscopic scale. A direct consequence is that the constitutive equation is only known for some flow conditions and given types of mixture. Here we have used a microstructural approach, which consists of considering the mixture as an effective continuum at the macroscopic level and inferring the bulk stress tensor from averaging of local interactions and local stresses. The bulk stress tensor may be split into elementary contributions pertaining to particle interactions. A complementary equation standing for the bulk energy dissipation may be needed in some circumstances. The analytical computation of these contributions is generally not possible. We present the various physical or heuristic reasonings usually proposed to circumvent this difficulty.