A Mixture of Two Micromorphic Materials

Abstract

Following the general paradigm developed by Twiss and Eringen [1], a model for the flow of a mixture of solid particulates dispersed in a fluid is developed. The theory has balance equations for mass, linear momentum, and angular momentum for each phase. The general constitutive theory is objective but does not satisfy the principle of equipresence. It does include non-linear constitutive equations for lift and drag. The major differences between this model and standard suspension models is the inclusion of constituent angular momentum balances and Magnus and shear lift in the constitutive equations. The theory is applied to Poiseuille flow for neutrally buoyant particulates. For just this simple setting, the theory reduces to five coupled non-linear equations in contrast to a single linear equation for a Newtonian fluid or two coupled linear equations for a micropolar fluid. A systematic parameter study of the solutions has been made and some typical profiles of the fluid velocity are shown. Generally, the presence of lift and drag tends to produce velocity profiles that are more parabolic when compared to cases when these effects are neglected. However, when strong boundary spin is prescribed, plug-shaped profiles can result.