Laminar flow in channels with porous walls

Abstract

An analytical solution for the axial and transverse flow fields in laminar flow in porous channels for both a rectangular channel with one porous wall and a porous tubular channel is presented. The solution is obtained from the Navier-Stokes equations without the simplifying assumption of constant permeation rate along the length of the duct. A dimensionless criterion for the validity of previous simplified solutions is developed which shows that the validity of the assumption of a constant permeation rate depends on the permeability of the membrane and the dimensions of the channel. Long channels with high permeability membranes can have significant departures from the constant permeation rate. The importance of these effects for the design of ultrafiltration and microfiltration modules is discussed.