Model of forward osmosis through composite/asymmetric membranes : effects of support inhomogeneity and solution non-ideality

The processes of Forward Osmosis and Pressure-Retarded Osmosis are strongly influenced by Internal Concentration Polarization occurring within their porous supports. Models of this important phenomenon usually assume that the support layer can be described by using a single space-independent value of effective diffusion coefficient of solute (or S-parameter). At the same time, FO/PRO supports are known to be not macroscopically homogeneous. Via a simple transformation of a modified convection-diffusion equation we show that the simple model with a constant effective diffusion coefficient is applicable to macroscopically inhomogeneous supports provided that this coefficient is understood as the harmonic average of the space-dependent one. Using the arithmetic average porosity leads to an overestimation of draw solute diffusivity within the support layer. The effects of draw solute non-ideality were explicitly and rigorously accounted for. We also demonstrate theoretically that the same harmonic average diffusive hindrance factor can be estimated from direct measurements of diffusion across the membrane supports if those are separately available. The effects of non-ideality are strongly dependent on draw solute choice. It is shown that, in the case of NaCl and KCl, draw solute non-ideality has fairly limited implications for FO and PRO flux prediction. In the case of MgSO4, non-ideality significantly influences expected fluxes: ignoring non-ideality leads to an overestimation of fluxes by a factor of two. In the case of MgCl2, despite strong solute non-ideality, the error is relatively limited, due to an increase of the osmotic coefficient offsetting a decrease of diffusivity as a function of MgCl2 concentration