PARTICLE DISTRIBUTION IN SUSPENSION SHEAR-FLOW

The model of this paper is based on an earlier proposed constitutive e quation that factors in all normal stresses originated by random parti cle fluctuations. This equation is used to describe the joint effect o f thermal and shear-induced fluctuations on concentrational distributi ons in suspension flow. Averaged products of fluctuation velocity comp onents are evaluated on the basis of a rational mechanics approach com bined with a simple kinematic consideration. The momentum conservation equation for the dispersed phase of a suspension closed by this const itutive equation is applied to unidirectional shear flow in the gravit y 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 fini te particle size, all other things being equal. Additionally, the deve loped model provides a reasonable explanation for the particle distrib utions observed in Couette flow. For these flows, the momentum conserv ation equation can also be reformulated to yield a diffusion-like equa tion for the suspended particles. However, coefficients of mutual diff usion due to both thermal and shear-induced fluctuations are drastical ly different from corresponding self-diffusivities as regards both the ir scaling and their concentrational dependence.