Modeling of particle trajectories in an electrostatically charged channel

Modeling and analyses of filtration efficiency in electrostatically charged monolith filters are important for evaluating and designing this class of filters. Unlike traditional fibrous filters which comprise external flow around a fiber, monolith filters are modeled as internal flow through small channels. Analogous to single fiber theory for external flows, single channel theory is used to analyze basic fluid mechanics in monolith filters and predict filtration efficiencies. The model incorporates three forces: hydrodynamic forces, electrostatic forces, and Brownian motion. Fluid velocity within the channels is calculated by using an analytical solution for circular channel flow, within which the slip boundary condition is considered because of small length scales. This velocity field is then used to evaluate the drag force on the particle according to Stokes's law. For this model, a one-way coupling between the fluid flow and the particle motion is assumed due to the fact that the relaxation time for the particles simulated in this paper is very small compared to the time the particles spend in the channel. The electrostatic field is computed assuming a uniform charge distribution on the inner surface of a cylindrical channel of finite length. Using a Monte Carlo simulation, particles are randomly injected into a single channel to determine the filtration efficiency.