Numerical modelling of mass transfer in slits with semi‐permeable membrane walls

A mathematical model to predict the concentration polarisation in nanofiltration/reverse osmosis is described. It incorporates physical modelling for mass transfer, laminar hydrodynamics and the membrane rejection coefficient. The SIMPLE algorithm solves the discretised equations derived from the governing differential equations. The convection and diffusive terms of those equations are discretised by the upwind, the hybrid and the exponential schemes for comparison purposes. The hybrid scheme appears as the most suitable one for the type of flows studied herein. The model is first applied to predict the concentration polarisation in a slit, for which mathematical solutions for velocities and concentrations exist. Different grids are used within the hybrid scheme to evaluate the model sensitivity to the grid refinement. The 55×25 grid results agree excellently for engineering purposes with the known solutions. The model, incorporating a variation law for the membrane intrinsic rejection coefficient, was also applied to the predictions of a laboratory slit where experiments are performed and reported, yielding excellent results when compared with the experiments.

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