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.

A frequency quantum interpretation of the surface renewal model of mass transfer

“…Using equation (2.11) and equations (3.1)–(3.11) yields the following: Equations (3.12) and (3.13) are mathematically similar to the expressions for permeate flux decline and cake mass build-up, respectively, in constant pressure, crossflow microfiltration [ 42 ]. It is further seen from these equations that in general.…”