Expression for critical suspended particle size in granular media filtration processes

The critical suspended particle size is defined as the suspended particle size with a minimum collector efficiency in a packed bed filter. Identification of the critical size particles is important when a granular filtration process is designed for removal of a mixture of suspended particles with different particle sizes. This note intends to derive a simple expression from the filtration model of Rajagopalan and Tien [Rajagopalan, R. and Tien, C. (1976) Trajectory analysis of deep-bed filtration with the sphere-in-a-cell porous media model. AIChE J. 2(3), 523–533.] for the critical particle size and to investigate the effects of temperature, suspended particle density, collector diameter and approach velocity on the critical particle size and the corresponding collector efficiency.