Permeability of porous materials determined from the Euler   characteristic
  We study the permeability of quasi two-dimensional porous structures of randomly placed overlapping monodisperse circular and elliptical grains. Measurements in microfluidic devices and lattice Boltzmann simulations demonstrate that the permeability is determined by the Euler characteristic of the conducting phase. We obtain an expression for the permeability that is independent of the percolation threshold and shows agreement with experimental and simulated data over a wide range of porosities. Our approach suggests that the permeability explicitly depends on the overlapping probability of grains rather than their shape. 
Christian Scholz, Frank Wirner, Jan G\"otz, Ulrich R\"ude, Gerd E.   Schr\"oder-Turk, Klaus Mecke, Clemens Bechinger
physics.flu-dyn cond-mat.mtrl-sci cond-mat.soft