Predicting permeate flux in ultrafiltration on the basis of surface renewal concept

Abstract

On the basis of a wide literature review it is concluded that the surface renewal concept is more appropriate than the film theory in describing mass transport phenomena at a membrane surface. The turbulence, lifting forces and drag forces (affected by the lateral flow of the permeate through the membrane pores), cause the stochastic nature of the hydrodynamical conditions at the membrane surface. The main obstacle in applying the surface renewal theory to a description of mass transfer at the membrane surrace is the problem of determining the instantaneous permeate flux J(t) in a single element of the freshly renewed membrane surface. Therefore it is recommended to apply the results of the unstirred batch cell experiments as a good approximation of J(t). Assuming surface renewal conditions after Danckwerts [Ind. Eng. Chem., 43 (1951) 1460], the overall permeate flux can be predicted as an average value involving age distribution of the elements of the membrane surface. This approach enables the uniform description of mass transfer in ultrafiltration over a wide range despite such problems as: the diffusive or nondiffusive nature of the solute; the osmotic or gel interpretation of flux limitation; difficulties with the exact solution of a nonlinear convective diffusion problem in the case of diffusive solutes; and which factor controls the flux (i.e. the membrane or the concentration polarization layer)? The method was verified experimentally using BSA solutions and kaolin suspension. The model is able to predict the “limiting flux” phenomenon which is very important in designing and controlling ultrafiltration processes.