Simulation of colloidal fouling by coupling a dynamically updating velocity profile and electric field interactions with Force Bias Monte Carlo methods for membrane filtration.

Pressure-driven flow through a channel with membrane walls is modeled for high particulate volume fractions of 10%. Particle transport is influenced by Brownian diffusion, shear-induced diffusion, and convection due to the axial crossflow. The particles are also subject to electrostatic double layer repulsion and van der Waals attraction, from both particle-particle and particle-membrane interactions. Force Bias Monte Carlo (FBMC) simulations predict the deposition of the particles onto the membranes, where both hydrodynamics and the change in particle potentials determine the probability that a proposed move is accepted. The particle volume fraction is used to determine an apparent local viscosity observed by the continuum flow. As particles migrate, the crossflow velocity field evolves in quasi-steady fashion with each time instance appearing fully developed in the downstream direction. Particles subject to combined hydrodynamic and electric effects (electrostatic double layer repulsion and van der Waals attraction) reach a more stable steady-state as compared to systems with only hydrodynamic effects considered. As expected, at higher crossflow Reynolds numbers more particles remain in the crossflow free stream.