A NUMERICAL-MODEL OF STEADY-STATE PERMEATE FLUX DURING CROSS-FLOW ULTRAFILTRATION

The mass transport mechanisms during cross-flow ultrafiltration (UF) a re mathematically expressed using the two-dimensional convective diffu sion equation where the axial diffusion term is neglected for an axial Peclet number much greater than the transverse Peclet number. A numer ical scheme is presented to solve the steady-state two-dimensional con vective diffusion equation for the case of known uniform permeate flux . However, in the actual cross-flow UF process, the permeate flux alon g the axial direction is unknown and usually decreases with axial dist ance. Therefore, an iterative algorithm is developed to predict the st eady-state permeate flux based on the assumption that the concentratio n at membrane surface cannot exceed a certain limiting value. Using th e numerical model with an effective diffusion coefficient, which is co nsidered to be the sum of molecular diffusion and shear-induced hydrod ynamic diffusion coefficients, the effects of particle size, feed conc entration, and axial velocity on the steady-state permeate flux were i nvestigated.