Clarification of clean-bed filtration models

Clean-bed filtration models are frequently used to make engineering calculations on aquasol removal in filters. They consist of a filtration equation, derived from a mass balance around a collector, a single-collector collision efficiency, and an empirically derived sticking coefficient. In order to be correctly applied and referenced, the two most commonly used models, the Yao model and the Rajagopalan and Tien (RT) model, require additional clarification. The filtration equation used in the Yao model has a different form than that of an aerosol counterpart due to assumptions made in choosing a reference velocity in the system. The RT model, as originally published, had variables hidden within constants and contained typographic errors. In this paper we identify the differences in the Yao and aerosol filtration model derivations, correctly present the RT model, and compare model predictions with particle removals reported in laboratory columns.