We investigate the dynamics of depth filtration, in which a dirty fluid is cleaned by trapping the suspended dirt particles within the pore space during flow through a porous medium. This process is investigated for simple pore geometries for which analytical calculations can be performed. Within such idealized models, we show that the trapped particles have a power-law density profile as a function of distance from the input point. We also determine the time until a filter becomes clogged. Using an extreme-value statistics approach, we argue that the distribution of times until a filter clogs has a power-law long-time tail, with an infinite mean clogging time. These results are in accord with simulations on a square lattice porous network.
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