SIMPLE-MODEL FOR DEEP BED FILTRATION

We present a simple model for deep bed filtration, where particles sus pended in a fluid are trapped while passing through a porous filter. A steady state of the model is reached when the filter cannot trap addi tional particles. We find the model has two qualitatively different st eady slates depending on the fraction of traps, and the steady states can be described by directed percolation. We study, in detail, the evo lution of the distribution of trapped particles, as the number of trap ped particles increases. To understand the evolution, we formulate a m ean field equation for the model, whose numerical solution is consiste nt with the behavior of the model. We find the trapped particle distri bution is insensitive to details of the formulation of the model.