Fluid Flow through Porous Media: The Role of Stagnant Zones

We investigate fluid flow through disordered porous media by direct simulation of the Navier-Stokes equations in a two-dimensional percolation structure. We find, in contrast to the log-normal distribution for the local currents found in the analog random resistor network, that over roughly 5 orders of magnitude the distribution $n\left(E\right)$ of local kinetic energy $E$ follows a power law, with $n\left(E\right)\propto E^{-\alpha }$, where $\alpha =0.90\mathrm{}\pm 0.03$ for the entire cluster, while $\alpha =0.64\mathrm{}\pm 0.05$ for fluid flow in the backbone only. Thus the “stagnant” zones play a significant role in transport through porous media, in contrast to the dangling ends for the analogous electrical problem.