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

We focus our attention on granular suspensions made up of noncolloidal sphe rical particles within a Newtonian fluid. The main objective of this paper is to provide a general framework for the formulation of the bulk stress te nsor. The bulk stress within granular suspensions is mainly generated at th e particle level by strong interactions between particles, such as friction , collision, and lubricated contact. The existence of a few local mechanism s is a major cause of behavior complexity at the macroscopic scale. A direc t 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 contin uum at the macroscopic level and inferring the bulk stress tensor from aver aging 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 n eeded in some circumstances. The analytical computation of these contributi ons is generally not possible. We present the various physical or heuristic reasonings usually proposed to circumvent this difficulty. (C) 1999 The So ciety of Rheology. [S0148-6055(99)01606-5].