Pressure-driven pipe flow of semi-dilute and dense suspensions over permeable surfaces

Abstract

We study pressure-driven suspensions of non-colloidal, non-Brownian, and rigid spheres in a Newtonian solvent where the pipe surface is replaced by porous media using numerical simulations. We examine various values of the permeability of the porous medium K, while we keep the porosity and the thickness of the porous layer constant to clarify the effect of the permeable wall on the suspension flows at bulk particle volume fractions 0.1 ≤ ϕ b ≤ 0.5. In the limit of vanishing inertia, the rate of suspension flow decreases as the bulk volume fraction ϕ b increases and it builds up as the permeability of the porous media increases. There are also two different regimes characterizing the dimensionless slip velocity normalized by both shear rate and penetration depth, namely, the strong permeability regime and the weak permeability regime. In the former, the solvent penetrates deeper and the streamwise velocity at the interface increases with the porous media permeability, while in the latter, the fluid cannot go through the porous media deeply and the variation of the slip velocity with the permeability is small. Our results might suggest a new passive technique to reduce drag by enhancing the rate of suspension flow in devices where the suspension transport is crucial. It might also offer basic insights for the extension to the flow of suspensions over and through complex porous media.