The interactions between porous media and fl uids fl owing through them are very intense, because the wetted perimeter to fl uid cross-section ratios are very large in porous media, relative to other examples of viscous fl ow in conduits. The principles of viscous fl uid fl owing in contact with confi ning surfaces (such as tubular conduits) were described in the early through mid-1800s, in a progression of theoretical developments by Navier, Hagen and Pouseuille and Stokes1. Collectively, they laid down a mathematical framework to calculate the resistance to viscous fl uid fl ow through porous media. However, natural aquifer matrices are too irregular to allow explicit mapping of the contact between fl owing groundwater and the porous medium. Without a matrix map, the mathematics of viscous fl ow cannot be applied directly to groundwater fl ow. Even for mappable matrices, such as packed beds of glass beads2, the mathematics of a Navier-Stokes analysis is quite daunting, beyond the capacities of desktop computers.