Non-equilibrium (irreversible) themodynamics is used to investigate colloidal back-diffusion during crossflow membrane filtration. The chemical potential is generalized as a superposition of equilibrium and irreversible contributions, originating from Brownian and shear-induced diffusion, respectively. As a result, an effective drag force is derived using the irreversible thermodynamics for a particle undergoing both Brownian and shear-induced diffusion in a sheared concentrated suspension. Using the drag force, a hydrodynamic force bias Monte Carlo method is developed for crossflow membrane filtration to determine the critical flux of hard sphere suspensions. Effects of shear rate and particle size on the critical flux are studied, and results show a good agreement with experimental observations reported in the literature.

Mixed matrix membranes of poly(vinyl alcohol) (PVA), loaded with phosphomolybdic heteropolyacid (HPA) and crosslinked with glutaraldehyde have been prepared by the solution casting technique. Pervaporation (PV) experiments have been performed at $30^{\circ}C$ to separate water-isopropanol feed mixtures containing 10 to 40 wt.% of water. The membranes were characterized by DSC and DMTA to understand their thermal behavior and mechanical strength properties. At high content (i.e. 7 wt.% with respect to weight of PVA) of HPA, the mixed matrix membranes could extract water efficiently on the permeate side with a selectivity of 90,000 and a flux of 0.032 $kg/m^2h$ for 10 wt.% of water containing feed mixture (the lowest feed composition of water studied). Flux of the mixed matrix membranes decreased with increasing concentrations of HPA.