Particle–particle interactions during normal flow filtration: Model simulations

Although particle trajectory calculations have been used previously to analyze the behavior of membrane systems, these studies have ignored the effects of particle–particle interactions. Particle motion was evaluated by numerical integration of the Langevin equation accounting for the combined effects of electrostatic repulsion, enhanced hydrodynamic drag, Brownian diffusion, and interparticle forces. In the absence of Brownian forces, particles are unable to enter the pore unless the drag force associated with the filtration velocity can overcome the electrostatic repulsion. The presence of a second particle alters the particle trajectories, forcing the particles to attain equilibrium positions located symmetrically about the pore centerline. Interparticle forces can effectively push the particle over the energy barrier, significantly reducing the magnitude of the critical filtration velocity required for particle transmission. Brownian forces also allow particles to enter the pore, with the particle transmission increasing with increasing filtration velocity.