  In biological transport mechanisms such as insect respiration and renal
filtration, fluid travels along a leaky channel allowing exchange with systems
exterior the the channel. The channels in these systems may undergo peristaltic
pumping which is thought to enhance the material exchange. To date, little
analytic work has been done to study the effect of pumping on material
extraction across the channel walls. In this paper, we examine a fluid
extraction model in which fluid flowing through a leaky channel is exchanged
with fluid in a reservoir. The channel walls are allowed to contract and expand
uniformly, simulating a pumping mechanism. In order to efficiently determine
solutions of the model, we derive a formal power series solution for the Stokes
equations in a finite channel with uniformly contracting/expanding permeable
walls. This flow has been well studied in the case of weakly permeable channel
walls in which the normal velocity at the channel walls is proportional to the
wall velocity. In contrast we do not assume weakly driven flow, but flow driven
by hydrostatic pressure, and we use Dacry's law to close our system for normal
wall velocity. We use our flow solution to examine flux across the
channel-reservoir barrier and demonstrate that pumping can either enhance or
impede fluid extraction across channel walls. We find that associated with each
set of physical flow and pumping parameters, there are optimal reservoir
conditions that maximizes the amount of material flowing from the channel into
the reservoir.
