Application of a surface-renewal model to permeate-flux data for constantpressure cross-flow microfiltration with dean vortices

Abstract

The introduction of flow instabilities into a microfiltration process can dramatically change several elements such as the surface-renewal rate, permeate flux, specific cake resistance, and cake buildup on the membrane in a positive way. A recently developed surface-renewal model for constant-pressure, cross-flow microfiltration (Hasan et al., 2013) is applied to the permeate-flux data reported by Mallubhotla and Belfort (1997), one set of which included flow instabilities (Dean vortices) while the other set did not. The surfacerenewal model has two forms ., the complete model and an approximate model. For the complete model, the introduction of vortices leads to a 53% increase in the surface- renewal rate, which increases the limiting (i.e., steady-state) permeate flux by 30%, decreases the specific cake resistance by 14.5% and decreases the limiting cake mass by 15.5% compared to operation without vortices. For the approximate model, a 50% increase in the value of surface renewal rate is shown due to vortices, which increases the limiting permeate flux by 30%, decreases the specific cake resistance by 10.5% and decreases the limiting cake mass by 13.7%. The cake-filtration version of the critical-flux model of microfiltration (Field et al., 1995) is also compared against the experimental permeate-flux data of Mallubhotla and Belfort (1997). Although this model can represent the data, the quality of its fit is inferior compared to that of the surface-renewal model.