As a filter (eg: in a washing machine) or a textile (eg: a raincoat) dries, any dirt or impurities in the water are left behind within the filter or the textile. It’s important for both these applications (and several more) to know where the dirt goes, because the deposited dirt can impact the future efficacy of the filter or raincoat. Does the dirt deposit uniformly throughout the porous material, or concentrate at the surface? Can the accumulating dirt ever clog the porespace entirely, and if so, how can we avoid this? To investigate, we use asymptotic analysis to derive an effective model for the motion of an evaporation front through a porous material, coupled with the accumulation, transport and deposition of the dirt.