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(E) of local kinetic energy E follows a power law, with n(E) proportional to E-alpha, where alpha = 0.90 +/- 0.03 for the entire cluster, while alpha = 0.64 +/- 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.