Modelling Collisional Stresses in a Dense Fluid-Solid Mixture

An idealized dense mixture of fluid and solid is considered. The mixture consists of identical spheres and a Newtonian fluid. Collisional stresses in a simple shear flow of such a mixture are quantified. These stresses are considered to be generated by binary collisions of spheres which result from the mean shear flow. The fluid is considered to act only as a dissipater of the fluctuating motion of the solids. Fluid stresses are neglected. Unlike previous analyses which make similar assumptions about the effect of the fluid, the present work does not require assumptions about the collision kinematics, except that the kinematics be homogeneous in the entire flow field. This is achieved by replacing analytical integrations with a Monte Carlo procedure. The resulting collisional stresses are found to increase and compare better with experimental data than previously obtained analytical results.