The impact of porous walls on the rheology of suspensions

TL;DR

This study investigates how isotropic porous walls affect the rheology of suspensions in plane Couette flow, revealing that increased wall permeability reduces effective viscosity and particle interactions.

Contribution

It provides a numerical analysis showing how porous walls decrease suspension viscosity and offers a closed-form equation to predict rheology with porous boundaries.

Findings

Porous walls decrease suspension effective viscosity.

Increased permeability leads to slip velocity at the interface.

Particle interactions and fluctuations are dampened.

Abstract

We study the effect of isotropic porous walls on a plane Couette flow laden with spherical and rigid particles. We perform a parametric study varying the volume fraction between $0$ and $30\%$, the porosity between $0.3$ and $0.9$ and the non-dimensional permeability between $0$ and $7.9 \times 10^{-3}$ We find that the porous walls induce a progressive decrease in the suspension effective viscosity as the wall permeability increases. This behavior is explained by the weakening of the wall-blocking effect and by the appearance of a slip velocity at the interface of the porous medium, which reduces the shear rate in the channel. Therefore, particle rotation and the consequent velocity fluctuations in the two phases are dampened, leading to reduced particle interactions and particle stresses. Based on our numerical evidence, we provide a closed set of equations for the suspension viscosity, which can be used to estimate the suspension rheology in the presence of porous walls.