Non-equilibrium Monte Carlo Simulations for Critical Flux of Hard Sphere Suspensions in Crossflow Filtration

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.