Interpretation and modeling of the averaged equations for a fluid-solid flow

A self-consistent derivation of the conservation laws is given for flows of a fluid-solid mixture. A unified analytical framework for obtaining constitutive relations is provided. This analysis uses a control volume/control surface approach that is widely used in fluid mechanics. All terms in the governing equations and the constitutive relations are written in terms of the mass-weighted averages except solid concentration. It is believed that the mass-weighted average is the natural bridge between micromechanics and constitutive relations. The derived momentum equations contain terms that differ from all existing models except that of Prosperetti and Jones (1984). However, their assumptions are not needed here. Special attention is given to the solid phase pressure. The physical basis of the previously assumed form for this pressure (Givler 1987) becomes clear. A number of related phenomena are also discussed. These include the anti-diffusion and anisotropic normal stresses. The energy equations are also different from existing models.