  We analyze the performance of membrane filters represented by pore networks
using two criteria: 1) total volumetric throughput of filtrate over the filter
lifetime and 2) accumulated foulant concentration in the filtrate. We first
formulate the governing equations of fluid flow on a general network, and we
model transport and adsorption of particles (foulants) within the network by
imposing an advection equation with a sink term on each pore (edge) as well as
conservation of fluid and foulant volumetric flow rates at each pore junction
(network vertex). Such a setup yields a system of partial differential
equations on the network. We study the influence of three geometric network
parameters on filter performance: 1) average number of neighbors of each
vertex; 2) initial total void volume of the pore network; and 3) tortuosity of
the network. We find that total volumetric throughput depends more strongly on
the initial void volume than on average number of neighbors. Tortuosity,
however, turns out to be a universal parameter, leading to almost perfect
collapse of all results for a variety of different network architectures. In
particular, the accumulated foulant concentration in the filtrate shows an
exponential decay as tortuosity increases.
