A one-velocity model of suspension flow through a high-porous medium

Abstract

Abstract A one-velocity model for slow flows of a suspension through a high-porous medium is proposed. The model involves the momentum equation (Brinkman equation) and two continuity equations for the suspension and suspended particles. The particle migration due to spatially varying frequency of particle-matrix collisions is heuristically accounted for. As other known diffusion models, the proposed one is not universal and is valid only for simple flow patterns (e.g., shear flows). A generalization of the proposed model for deep bed filtration is also given.