  Pore-size gradients are often used in the design of membrane filters to
increase filter lifetime and ensure fuller use of the initial membrane pore
volume. In this work, we impose pore-size gradients in the setting of a
membrane filter with an internal network of interconnected tube-like pores. We
model the flow and foulant transport through the filter using the
Hagen-Poiseuille framework coupled with advection equations via conservation of
fluid and particle flux, with adsorption as the sole fouling mechanism. We
study the influence of pore-size gradient on performance measures such as total
filtrate throughput and accumulated contaminant concentration at the membrane
downstream pore outlets. Within the limitations of our modeling assumptions we
find that there is an optimal pore-radius gradient that maximizes filter
efficiency independent of maximum pore length (an input parameter that
influences the structure of the pore network), and that filters with longer
characteristic pore length perform better.
