  Transport of viscous fluid through porous media is a direct consequence of
the pore structure. Here we investigate transport through a specific class of
two-dimensional porous geometries, namely those formed by fluid-mechanical
erosion. We investigate the tortuosity and dispersion by analyzing the first
two statistical moments of tracer trajectories. For most initial
configurations, tortuosity decreases in time as a result of erosion increasing
the porosity. However, we find that tortuosity can also increase transiently in
certain cases. The porosity-tortuosity relationships that result from our
simulations are compared with models available in the literature. Asymptotic
dispersion rates are also strongly affected by the erosion process, as well as
by the number and distribution of the eroding bodies. Finally, we analyze the
pore size distribution of an eroding geometry. The simulations are performed by
combining a high-fidelity boundary integral equation solver for the fluid
equations, a second-order stable time stepping method to simulate erosion, and
new numerical methods to stably and accurately resolve nearly-touching eroded
bodies and particle trajectories near the eroding bodies.
