Abstract
A rigorous dynamic mathematical model for predicting the rate of ultrafiltration of proteins has been developed. The model is based on sophisticated descriptions of the protein-protein interactions within the layer close to the membrane surface which are responsible for controlling permeation rate. Electrostatic interactions are accounted for by a Wigner-Seitz cell approach, including a numerical solution of the nonlinear Poisson-Boltzmann equation. London-van der Waals forces are calculated using a computationally efficient means of approximating screened, retarded Lifshitz-Hamaker constants. Configurational entropy effects are calculated using an equation of state giving excellent agreement with molecular dynamic data. Electroviscous effects are also taken into account. These descriptions of protein-protein interactions are used to develop an a priori model, with no adjustable parameters, that allows quantitative prediction of the rate of filtration of proteins as a function of zeta potential (and hence pH), ionic strength, applied pressure, protein size, and membrane resistance. A comparison with experimental data for the filtration of bovine serum albumin (BSA) shows that the model is in excellent agreement with such data.
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