Understanding the operation of filters used to remove particulates from fluids is important in many practical industries. Typically the particles are larger than the pores in the filter so a cake layer of particles forms on the filter surface. Here we extend existing models for filter blocking to account for deformation of the filter material and the cake layer due to the applied pressure that drives the fluid. These deformations change the permeability of the filter and the cake and hence the flow. We develop a new theory of compressible-cake filtration based on a simple poroelastic model in which we assume that the permeability depends linearly on local deformation. This assumption allows us to derive an explicit filtration law. The model predicts the possible shutdown of the filter when the imposed pressure difference is sufficiently large to reduce the permeability at some point to zero. The theory is applied to industrially relevant operating conditions, namely constant flux, maximising flux and constant pressure drop. Under these conditions, further analytical results are obtained, which yield predictions for optimal filter design with respect to given properties of the filter materials and the particles.
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