Depth filtration approach to the theory of standard blocking: Prediction of membrane permeation rate and selectivity

A macroscopic depth filtration theory for the standard blocking of the pores of UF/MF membrane is developed. The theory predicts the membrane permeation rate and selectivity based on the introduction of the classical filter coefficient and shows that the profile of the number of deposited particles over the pore length is highly nonuniform (steep), descending to the pore outlet. It is shown that the conventional standard blocking theory based on the uniform-profile assumption cannot adequately describe the variation of permeation rate with time for highly selective membranes and therefore should not be used in processing the experimental data. The adequate description of standard blocking can be obtained with simple analytical formulas derived on the basis of the developed depth filtration theory and the simplified model in which the actual steep profile is replaced by a stepwise profile of deposited particles. Comparison with experimental data showed a high accuracy of the proposed calculation formulas.