Numerical Study on the Impact of DC Electric Field on Fouling Characteristics of Cross-Flow Filtration

Applying numerical methods for predicting cake formation and development in cross-flow membrane filtration has been an area of research. The solutions, which are mainly based on the development of zero, one, or two-dimensional methods for estimating filtration parameters, have always suffered from an obvious need for some calibration steps. In this paper, an independent two-way solving method is presented to determine the time variation of the geometry of the cross-flow filtration cake, so that by simultaneously solving the flow through the lattice Boltzmann (LB), it is possible to solve the convection-diffusion equation, using another mesoscopic method (LB-CA) in a two way coupling manner between flow changes and cake growth. Applying LB-CA provides it for all kinds of internal and external forces effects on particles trajectories to be explicitly taken into account. The proposed model was validated against both of theory of Romero and Davis and some experimental results. Moreover, the model was used to determine external effects which are arisen from static imposition of a DC electric field, on cross-flow filtration outcomes. The calculated results exhibits considerable improvements in flux decline curve and removing of fouling in some areas along the membrane length, as DC voltage rises. Also, optimal conditions with considering the electric poles’ size as an optimization parameter shows that with considering the maximum improvement in the flux curve as the target parameter, the electric poles’ size has an optimal value.