Distributions of critical flux: modelling, experimental analysis and consequences for cross-flow membrane filtration

This paper discusses the consequences of possible distribution of critical flux (DCF) in cross-flow filtration. These distributions are described here by a normal function with a mean critical flux and its standard deviation. The DCF model allows the description, through an analytical relationship, of the variation in steady state permeate flux with trans-membrane pressure. Both strong and weak forms of critical flux, which can be observed on a membrane operating in cross-flow mode, are depicted. A simple graphical method to determine the mean critical flux and its standard deviation from experimental results is derived from the theoretical model. The theoretical trends are compared to experimental data and show good agreement for cross-flow filtration of latex and BSA suspensions. The distribution function parameters obtained by fitting the DCF model to experiments are compared to critical flux measured via a pressure step method. We thus propose a tool to analyse filtration results and to determine new global parameters for critical conditions (mean value and its standard deviation), which appears to be a good way to account for fouling complexity.