Relating forward water and reverse salt fluxes to membrane porosity and tortuosity in forward osmosis: CFD modelling

A 2D finite element model was developed to describe the forward osmosis (FO) process under steady-state conditions. Two approaches are applied to study forward water and reverse salt fluxes. In the first approach, the mathematical equations are formulated based on the bulk concentration differences between the feed and the draw solutions. Transfer resistances arising from internal concentration polarization, external concentration polarization and reverse salt flux are considered. The second approach is based on a complete computational fluid dynamic (CFD) model, both the constrictivity factor and the sorption coefficient are considered to enhance the accuracy of prediction. The CFD model provides a more realistic representation of the FO process than the first simple approach. Our CFD model shows that the concentration profile within the membrane support layer is a result of the coupled interaction between the dilutive internal concentration polarization and the reverse solute diffusion from the draw. Increasing porosity or decreasing tortuosity is not always desirable since it will also increase reverse salt flux. Forward water and reverse salt fluxes are independent on tortuosity or porosity alone, but dependent on their ratios. This work offers significant insights into developing high performance FO membranes with suitable porosity and tortuosity, thereby reducing internal concentration polarization and reverse salt diffusion.