Gradient clogging in depth filtration

We investigate clogging in depth filtration, in which a dirty fluid is ``cleaned'' by the trapping of dirt particles within the pore space during flow through a porous medium. This leads to a self-generated gradient percolation process that exhibits a power-law distribution for the density of trapped particles at downstream distance x from the input. To achieve a nonpathological clogging (percolation) threshold, the system length L should scale no faster than a power of lnw, where w is the system width. Nontrivial behavior for the permeability arises only in this extreme anisotropic geometry.