Asymptotic Solution of Mass Transfer in Parallel Plate Membrane Filtration Processes

Abstract

Asymptotic perturbation technique was applied to mass transfer in parallel plate membrane filtration processes on the basis of Berman's analytic solution of flow fields by assuming that the filtration flow velocity is constant. Pressure-driven and diffusive membrane transport was treated under the assumption that the axial length scale is sufficiently larger than the channel width. An ordinary differential equation for the solute permeation flux and the solute concentration at the membrane surface was derived from the mass balance equation by perturbation analysis. On the basis of the asymptotic ordinary differential equation, approximate solutions of overall mass transfer coefficient and Sherwood number were obtained under the homogeneous boundary condition that the solute concentration outside of the membrane is zero. Validity of the derived results was confirmed by comparing them with a series solution derived from eigenfunction expansion in the asymptotic state in which the filtration flux is sufficiently low. The proposed asymptotic method refines the conventional film theory and can be applied to mass transfer modeling of a variety of membrane filtration processes including low Reynolds number flow systems.