AbstractThe 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 surface-renewal 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.

Abstract This work examines the influence of the residence-time distribution (RTD) of surface elements on a model of cross-flow microfiltration that has been proposed recently (Hasan et al., 2013). Along with the RTD from the previous work (Case 1), two other RTD functions (Cases 2 and 3) are used to develop theoretical expressions for the permeate-flux decline and cake buildup in the filter as a function of process time. The three different RTDs correspond to three different startup conditions of the filtration process. The analytical expressions for the permeate flux, each of which contains three basic parameters (membrane resistance, specific cake resistance and rate of surface renewal), are fitted to experimental permeate flow rate data in the microfiltration of fermentation broths in laboratory- and pilot-scale units. All three expressions for the permeate flux fit the experimental data fairly well with average root-mean-square errors of 4.6% for Cases 1 and 2, and 4.2% for Case 3, respectively, which points towards the constructive nature of the model - a common feature of theoretical models used in science and engineering.

A mathematical model using classical cake-filtration theory and the surface-renewal concept is formulated for describing cross-flow microfiltration under dynamic and steady-state conditions. The model can predict the permeate flux and cake buildup in the filter. The three basic parameters of the model are the membrane resistance, specific cake resistance and rate of surface renewal. The model is able to correlate experimental permeate flow rate data in the microfiltration of fermentation broths in laboratory- and pilot-scale units with an average root-mean-square (RMS) error of 4.6%. The experimental data are also compared against the critical-flux model of cross-flow microfiltration, which has average RMS errors of 6.3, 5.5 and 6.1% for the cases of cake filtration, intermediate blocking and complete blocking mechanisms, respectively.