Rheology of particle suspensions with low to moderate fluid inertia at finite particle inertia

The lattice Boltzmann method is applied to simulate the rheology of particle suspensions with low-to-moderate fluid inertia and a wide range of particle inertia. The viscous dissipation in a suspension of particles with a Maxwellian velocity distribution is shown to have a linear dependence on the Reynolds number similar to the Ergun correlation for the drag in a fixed bed of particles. Dynamic simulations of the flow of a suspension of elastic particles being sheared between two rough walls are used to determine the range of Reynolds and Stokes numbers for which a treatment of a homogeneous, sheared suspension based on kinetic theory and the simulated viscous dissipation can accurately describe the particle-phase kinetic energy and effective viscosity of the suspension. The dependence of the particle-phase slip velocity and the depletion of particles near the boundaries on the particle volume fraction and Stokes number is determined.