Theoretical analysis of particle trajectories and sieving in a two-dimensional cross-flow filtration system

Particle deposition and fouling are critical factors governing the performance of microfiltration systems. Particle trajectories in cross-flow filtration were evaluated by numerical integration of the Langevin equation accounting for the combined effects of electrostatic repulsion, enhanced hydrodynamic drag, Brownian diffusion, inertial lift and van der Waals attraction. The membrane remains completely free of particles below a critical filtration velocity due to the electrostatic repulsion between the charged particles and the charged membrane. This critical flux increases with increasing surface potential and decreasing ionic strength due to the increase in electrostatic repulsion. The critical flux also increases with increasing wall shear rate due to the reduction in residence time over the pore. Brownian motion provides a random character to the particle trajectories, allowing particles to enter the pores even at operation below the critical flux. Particle transmission increases with increasing filtrate flux and ionic strength, and decreases with increasing particle size, wall shear rate and electrostatic potential.