The effects of flow rate on membrane capacity: Development and application of adsorptive membrane fouling models

Whereas it is common practice in the pharmaceutical industry to test candidate membranes for the purification of protein therapeutics in small-scale devices under constant pressure, the actual industrial use of these membranes in large-scale devices often involves conditions of constant flow. Previously, obtained data indicate that the rate of membrane fouling (and thus membrane capacity) depends upon flow rate, thus making it difficult to extrapolate membrane capacities for large-scale, constant flow conditions from measurements in small-scale, constant pressure devices. Here, we develop theoretical models of membrane fouling that incorporate flow rate dependence into the rate of pore plugging. The models assume that pore radius decreases as foulants deposit at the pore walls with zeroth-order kinetics and invokes the Hagen-Poiseuille equation for laminar flow in cylindrical tubes to obtain equations for flux and filtered volume as functions of time. The combined models provided good fits of the dependence of capacity on flux for a range of data and yielded accurate predictions of constant flux capacity data using parameters obtained from constant pressure data and vice versa. The models developed here should be useful industrial tools for predicting membrane capacities for constant flow conditions from constant pressure data and vice versa for a variety of combined fouling mechanisms.