The focus of this paper is on the mechanisms and modelling of flux decline. Three distinct forms of modelling flux decline of cross flow filtration at constant transmembrane pressure (ΔP) were examined. The best fit to the data sets examined was obtained with the model developed previously by Field [9,10]. The general equation is (dJ/dt)=−kj (J−J*) J(2−n) where n depends upon the fouling mechanism and J* is the steady-state flux. This approach to the analysis of flux data has the ability to identify the dominant mechanism, which has been shown to depend upon the membrane used and the operating conditions. In order not to give undue emphasis to early or late times, the data were fitted in both flux and resistance form simultaneously. The dominant fouling mechanism was found to be either incomplete pore blocking (n=1) or ‘cake’ filtration (n=0). Trends in the model parameters are also discussed in relation to operating conditions such as mode of filtration, cross-flow velocity and transmembrane pressure. For dead-end filtration, the initial rate of flux decline was found to be proportional to ΔP, as suggested by theory. The model of Wu et al. was shown to have limited predictive performance and discarded as being empirical. The model of Koltuniewicz was shown to have limited application and unrealistic performance in this filtration application. The two most significant practical observations on the oily-water data are (1) the initial rate of fouling is significantly lower for cross-flow velocities of 0.8 ms−1 or greater and (2) a ΔP of 1 bar can lead to excessive fouling. With regard to microfiltration modelling generally, further comparison between the three models with other data sets is recommended.
Arnot, T., Field, R. W., & Kolutniewicz, A. B. (2000). Cross–flow and dead–end microfiltration of oily–water emulsion. Part II: Mechanisms and modelling of flux decline. Journal of Membrane Science, 169(1), 1-15. https://doi.org/10.1016/S0376-7388(99)00321-X