Shadow Effect and Filtration Efficiency of a Granular-Bed Filter

Abstract

The filtration efficiency of a granular-bed filter is classically computed under the assumption that the collected particles are completely remixed after each layer of collectors, and thus the single-collector efficiency model may be repeatedly applied to each and every layer. Comparisons of total filter efficiencies obtained experimentally for filters that differ only in their respective lengths indicate this assumption to be wrong. Filters of different lengths yield different values for the single-collector efficiencies when classically checked. The present investigation examines the shadowing affect of one layer on the performance of the next one, taking into account the fact that a region swept by a collector may include parts already depleted of particles by a previous collector. Since the details of the construction of the granular-bed filter are in general not known, there seems to be no deterministic way to formulate the distribution of particle-free regions in the gas behind each collector layer. The distribution is therefore assumed Gaussian, with a standard deviation computed to fit the experimental data. Available experimental data indicate that this investigation indeed yields one single-collector efficiency for filters which differ only by their lengths. For standard deviations which exceed 0.5 the present investigation approaches asymptotically the classical theory; i.e., the shadow effect becomes negligible.