Prediction of solute rejection and modelling of steady-state concentration polarisation effects in pressure-driven membrane filtration using computational fluid dynamics

A two-dimensional (2D) steady state numerical model of concentration polarisation (CP) phenomena in a membrane channel has been developed using the commercially available computational fluid dynamics (CFD) package CFX (Ansys, Inc., USA). The model incorporates the transmembrane pressure (TMP), axially variable permeate flux, variable diffusivity and viscosity, and osmotic pressure effects. The model has been verified against several benchmark analytical and empirical solutions from the membrane literature. Additionally, the model is able to predict the rejection of an arbitrary solute by the membrane using a pore model, given some basic knowledge of the geometry of the solute molecule or particle, and the membrane pore geometry. This allows for predictive design of membrane systems without experimental determination of the membrane rejection for the specified operating conditions. A demonstration of the model is presented against experimental results for two uncharged test compounds (sucrose and PEG1000) from the literature. The model will be extended to incorporate charge effects, transient simulations, three-dimensional (3D) geometry and turbulent effects in future work.