Asymptotic analysis of the growth of cake layers in filters

The problem of fluid flow in a two-dimensional pleated filter is considered. Of particular interest is the change in the flow due to cake build-up on the surface of the filter material. The flow is taken to be Darcy flow in the cake and the filter material, with Stokes' flow outside the cake. The particles in the flow are taken to be transported with the flow and to stick to the cake without slippage or resuspension, and the cake is taken to be incompressible. The flow is considered in various geometries, particularly long thin filters and corners. The main parameter in the problem is the ratio of the filter-material resistance to the cake resistance, and limiting cases are considered. Travelling waves of cake build-up are found for arbitrary time-dependent variations in the inflow conditions. The time taken for the filter to become clogged by the cake is also considered.