Deposition of Brownian Particles on Cylindrical Collectors in a Periodic Array

The capture of charged Brownian particles in an idealized square array of cylindrical collectors has been studied using a finite element method. In addition to varying the size of the cylindrical collectors and the porosity, the collector-particle interactions resulting from van der Waals attraction and electrostatic repulsion have been considered. In a typical filtration process where the particle capture is diffusion-limited, a critical value of surface potential appears to exist above which the filter coefficient decreases rapidly. It is due to the insurmountable repulsive barrier between the particles and collectors. While the value of the critical surface potential varies with the electrolyte concentration and the Hamaker constant, it apparently corresponds to a common value of about 10 kT for the height of the primary maximum of the interaction potential.