  Filtration of feed containing multiple species of particles is a common
process in the industrial setting. In this work we propose a model for
filtration of a suspension containing an arbitrary number of particle species,
each with different affinities for the filter membrane. We formulate a number
of optimization problems pertaining to effective separation of desired and
undesired particles in the special case of two particle species and we present
results showing how properties such as feed composition affect the optimal
filter design (internal pore structure). In addition, we propose a novel
multi-stage filtration strategy, which provides a significant mass yield
improvement for the desired particles, and, surprisingly, higher purity of the
product as well.
