  A filter comprises porous material that traps contaminants when fluid passes
through under an applied pressure difference. One side-effect of this applied
pressure, however, is that it compresses the filter. This changes the
permeability, which may affect its performance. As the applied pressure
increases the flux of fluid processed by the filter will also increase but the
permeability will decrease. Eventually the permeability reaches zero at a point
in the filter and the fluid flux falls to zero. In this paper we derive a model
for the fluid transport through a filter due to an applied pressure difference
and the resulting compression. We use this to determine the maximum operating
flux that can be achieved without the permeability reaching zero and the filter
shutting down. We determine the material properties that balance the desire to
maximize flux while minimizing power use. We also show how choosing an initial
spatially dependent permeability can lead to a uniformly permeable filter under
operation and we find the permeability distribution that maximizes the flux for
a given applied pressure, both of which have desirable industrial implications.
The ideas laid out in this paper set a framework for modelling more complex
scenarios such as filter blocking.
