A constitutive model for microstructure and total stress in particulate suspensions

Constitutive equations for concentrated suspensions that explicitly account for the development of anisotropy in the microstructure are not generally available, even for relatively simple systems of hard spheres suspended in a Newtonian medium. Here, we use a directionally dependent mean-free path length and a truncated Cartesian tensor expansion to define a second-order structure tensor for systems of suspended particles. This tensor captures the principal nature of the microstructure. A sermempirical differential equation is developed for the structure tensor, with representation theorems being used to insure frame indifference. A separate equation is proposed to relate the stress tensor to the structure and rate of strain tensors. These coupled equations model structure and stress in both steady and time-dependent viscometric flows. Results from Stokesian dynamics simulations are used to demonstrate the utility of this modeling approach. The simulations were for monodisperse suspensions in an infinite shear field, and included hydrodynamic and short-ranged repulsive forces between the particles. Steady-state results and model fit are emphasized. (c) 2006 The Society of Rheology.