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.

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Analyzing trajectories of particles in monolith filters is important for predicting the capture efficiency and improving the design of this class of filters. Modeling and simulations of the particle trajectories are carried out to evaluate the probability of capture by the filter’s front surface and filter channel’s inner wall. Due to Brownian motion and electrostatic attraction, the particles exhibit a random walk and their trajectories deviate from the streamlines of the fluid flow. Particle trajectories are computed by the integration of Newton’s second law, where the electrostatic force, the Brownian motion force resulting from random collisions of the particle with air molecules, and the drag force from the surrounding fluid are all taken into account. A computer simulation for computing the particle trajectories and evaluating the probability of particle capture by the filter was developed. For this model, both flow field and electric field must be provided. The electric charge was assumed to be uniformly distributed along the edge of the channels of the filter and calculated numerically. The flow field is difficult to obtain due to the complex geometry of the model. The commercial CFD package ANSYS CFX [1] is used to compute the flow field. The resulting velocity flow field is then used to evaluate the drag force on the particles. We assume a one-way coupling between the fluid flow and the particle motion. Although there can be over one million uniformly distributed channels per square centimeter in the monolith filter, for simulation purposes, a single unit cell which models only one channel is used. The single unit model effectively describes the behavior of particles outside and inside the channels of monolith filter. The effects of different forces and different particle sizes were analyzed to investigate which factors affect the capture efficiency.