Laminar flow in channels with porous walls, revisited

An analytical solution for the pressure drop in fluid flow in a rectangular slit and cylindrical tube with porous walls is presented for the case of constant wall permeability. It is shown that model predictions for the particular case of constant wall velocity for rectangular slit with permeable walls agrees very well with Berman’s solution [J. Appl. Phys. 24 (1953) 1232]. The derivation presented in this work leads to analytical expressions for pressure drop as a function of wall permeability, channel dimension, axial position and fluid properties. These analytical expressions for constant wall permeability could be used to benchmark numerical routines for fluid flow modeling past semi-permeable membranes and for quick engineering estimates for pressure drop in cross-flow membrane modules.