Theoretical analysis of the influence of the axial variation of the transmembrane pressure in cross-flow filtration of rigid spheres

A model of the axial and the radial transmembrane pressure drop in a cylind rical cross-flow filtration module was developed by performing a hydrodynam ic analysis of the fluid flow based on the momentum and the continuity equa tions. Use of this expression for the transmembrane pressure drop together with the resistance model and the concept of shear induced diffusion of the particles at the membrane surface resulted in an expression of the permeat e flux. The predictions of the transmembrane pressure drop, the permeate fl ux and the particles near the membrane surface are discussed for cases with and without the formation of a stagnant layer The importance of the cylind rical membrane fiber dimensions on the permeate flux is also discussed. (C) 1999 Elsevier Science B.V. All rights reserved.