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Ultrafiltration of macromolecular solutions and cross-flow microfiltration of colloidal suspensions. A contribution to permeate flux calculations

Journal of Membrane Science
Publication Date
DOI: 10.1016/0376-7388(88)80020-6


Abstract Ultrafiltration and cross-flow microfiltration are pressure-driven membrane processes which exhibit concentration polarisation in front of the membrane or gel layer, respectively. In ultrafiltration the concentration polarization is essentially determined by diffusion in the boundary layer. With the usual assumption of constant material properties, the film theory predicts fluxes quite accurately in the case of ultrafiltration of low molecular weight solutions. The calculated fluxes are, however, significantly lower than the observed figures in case of ultrafiltration of macromolecular solutions. It will be shown that with concentration-dependent material properties, especially a variable density (!) and a variable diffusion coefficient, the film theory can predict fluxes of ultrafiltration of macromolecular solutions very accurately. Such a theory fails, however, in case of cross-flow filtration of colloidal suspensions. Even with the assumption of a variable density in the boundary layer, the calculated fluxes are too low by a factor of about 10. For cross-flow microfiltration of colloidal suspensions, a model is presented considering basically the membrane-parallel drag forces acting on a particle in the vicinity of the membrane and a “friction” force as a consequence of the lateral drag forces. The model has been tested with different module systems and with different colloidal suspensions.

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