Universal scaling for the permeability of random packs of overlapping and nonoverlapping particles
Jérémie Vasseur, Fabian B. Wadsworth, Eloïse Bretagne, Donald B. Dingwell
Abstract
Constraining fluid permeability in porous media is central to a wide range of theoretical, industrial, and natural processes. In this Letter, we validate a scaling for fluid permeability in random and lattice packs of spheres and show that the permeability of packs of both hard and overlapping spheres of any sphere size or size distribution collapse to a universal curve across all porosity $\ensuremath{\phi}$ in the range of ${\ensuremath{\phi}}_{c}<\ensuremath{\phi}<1$, where ${\ensuremath{\phi}}_{c}$ is the percolation threshold. We use this universality to demonstrate that permeability can be predicted using percolation theory at ${\ensuremath{\phi}}_{c}<\ensuremath{\phi}\ensuremath{\lesssim}0.30$, Kozeny-Carman models at $0.30\ensuremath{\lesssim}\ensuremath{\phi}\ensuremath{\lesssim}0.40$, and dilute expansions of Stokes theory for lattice models at $\ensuremath{\phi}\ensuremath{\gtrsim}0.40$. This result leads us to conclude that the inverse specific surface area, rather than an effective sphere size or pore size is a universal controlling length scale for hydraulic properties of packs of spheres. Finally, we extend this result to predict the permeability for some packs of concave nonspherical particles.