Hydrodynamic interactions and mean settling velocity of porous particles in a dilute suspension

Abstract

A theoretical investigation is conducted to study hydrodynamic interactions among porous spheres under creeping flow conditions. The particles may differ in size and permeability. Based on the Brinkman equation governing the fluid flow inside the particle, the flow field, and the drag force and torque on the particle are calculated numerically using a boundary collocation method. The results show that the hydrodynamic interaction increases with decreasing permeability. An important feature is that unlike the singular force and torque for two touching identical impermeable spheres undergoing certain motions with planar symmetry, the force and torque always remain finite for the case of two porous spheres. Using the resulting hydrodynamic interactions, the average sedimentation velocity of porous spheres suspended in a bounded fluid is also evaluated to determine the leading order effect of the particle concentration. Because of weaker hydrodynamic interactions among porous spheres, the hindrance coefficient is smaller than that for impermeable particles. When the porous spheres carry charge, the hindrance effect is augmented by increasing the double layer thickness.