Optimising the flow through a concertinaed filtration membrane

Membrane filtration is a vital industrial process, with applications
including air purification and blood filtration. In this paper, we study the
optimal design for a concertinaed filtration membrane composed of angled porous
membranes and dead-ends. We examine how the filter performance depends on the
angle, position, thickness, and permeance of the membrane, through a
combination of numerical and asymptotic approaches, the latter in the limit of
a slightly angled membrane. We find that, for a membrane of fixed angle and
physical properties, there can exist multiple membrane positions that maximise
the flux for an applied pressure difference. More generally, we show that while
the maximal flux achievable depends on the membrane thickness and permeance,
the optimal membrane configuration is always in one of two setups: centred and
diagonal across the full domain; or angled and in the corner of the domain.