Particle distribution in suspension shear flow

The model of this paper is based on an earlier proposed constitutive equation that factors in all normal stresses originated by random particle fluctuations. This equation is used to describe the joint effect of thermal and shear-induced fluctuations on concentrational distributions in suspension flow. Averaged products of fluctuation velocity components are evaluated on the basis of a rational mechanics approach combined with a simple kinematic consideration. The momentum conservation equation for the dispersed phase of a suspension closed by this constitutive equation is applied to unidirectional shear flow in the gravity field and to rotational Couette flow. Coupling the thermal and shear-induced fluctuations results in a situation where the total volume of particles suspended in a given shear flow reaches a minimum at a finite particle size, all other things being equal. Additionally, the developed model provides a reasonable explanation for the particle distributions observed in Couette flow. For these flows, the momentum conservation equation can also be reformulated to yield a diffusion-like equation for the suspended particles. However, coefficients of mutual diffusion due to both thermal and shear-induced fluctuations are drastically different from corresponding self-diffusivities as regards both their scaling and their concentrational dependence.