  Pleated membrane filters, which offer larger surface area to volume ratios
than unpleated membrane filters, are used in a wide variety of applications.
However, the performance of the pleated filter, as characterized by a
flux-throughput plot, indicates that the equivalent unpleated filter provides
better performance under the same pressure drop. Earlier work (Sanaei &
Cummings 2016) used a highly-simplified membrane model to investigate how the
pleating effect and membrane geometry affect this performance differential. In
this work, we extend this line of investigation and use asymptotic methods to
couple an outer problem for the flow within the pleated structure to an inner
problem that accounts for the pore structure within the membrane. We use our
new model to formulate and address questions of optimal membrane design for a
given filtration application.
