Simple Filtration Using Porous Media

This work is a study of the movement of particles, one at a time, through a fixed filter. Various assumptions are made about particle and pore sizes, pore selection rules and filter configurations. This report is divided into three main sections: The first studies the filter by analyzing its layers both in a qualitative sense and by computational simulations. The next studies the filter through a set of continuum models. The last consider a network model. In the layer model a porous media is represented as a rectangular array, with each point in the array representing a single pore in the media. This divides the media into a series of layers, with the same number of pores in each layer. When a particle encounters the media it selects a pore from the first layer. If the particle diameter is greater than or equal to the width of the pore then the particle clogs that pore, and the pore is no longer available for future particles. If the particle is smaller than the pore then it passes through to the next layer and now a pore in the next layer is chosen and the process continues until either the particle leaves the media, or gets stuck in a pore. One of the most important issues that must be determined in a layer model of a filter is the spread. The spread is the set of pores in the (n+1)-st layer that can be reached by a particle which has made it through a larger pore in the n-th layer. The two opposite extreme choices are, on the one hand, to assume that the particle can only move straight through to the pore directly below, or on the other hand, to assume that the particle can reach all pores in the next layer below. Both of these extremes seem problematic, though one might imagine a model where all pores are reachable