Channel Flow of a Mixture of Granular Materials and a Fluid

In this paper, we consider the three dimensional flow of granular materials and a viscous fluid in a channel. We use Mixture Theory to treat this problem as a two-component system [1]: One component is the solid particles (granular materials), such as sand, coal particles or red blood cells; the solid particles are modeled as a generalized Reiner-Rivlin type fluid derived by Massoudi [2], which not only considers the effects of volume fraction but also has a viscosity which is shear rate dependent. The other component, the host fluid, is assumed to behave as a linear viscous fluid, such as water, oil or plasma. For the interaction forces, the effect of different hindrance functions for the drag force is studied; moreover a generalized form of the expression for the hindrance function is suggested. For studying this two-component system numerically, a three dimensional CFD solver based on OpenFOAM® has been developed. Applying this solver, a specific problem (blood flow) has been studied for which our numerical results and experimental data [3] show good agreement.