Together with Robert Ziff and Salvatore Torquato, I determined the void percolation thresholds around hard and overlapping sphere models, including MRJ sphere packings and our amorphous inherent structures of the quantizer energy. The latter have a remarkably low critical porosity.
M. A. Klatt, R. M. Ziff, S. Torquato. Critical pore radius and transport properties of disordered hard- and overlapping-sphere models. Phys. Rev. E 104:014127-1–10 (2021).
Fluid flow through porous media plays a crucial role in many applications, from groundwater hydrology to industrial filtration. Our aim is to find convenient yet reliable estimates of the fluid permeability based on the structural and topological characteristics of the complex tortuous pore space. Such predictions can facilitate the design of porous media with desirable transport properties. For porous media with a well-connected pore space, a recent study suggested the second moment of the pore-size distribution as a convenient alternative to the often-used critical pore radius, which requires a sophisticated percolation analysis. We determine both descriptors for disordered and ordered model microstructures, including maximally random jammed (MRJ) spheres, overlapping spheres, equilibrium hard spheres, quantizer configurations, and lattice packings. Interestingly. we find that the second moment of the pore-size distribution is — to a good approximation — proportional to the critical pore radius. In fact, in contrast to the latter, the former predicts the correct ranking of the permeability for our models. Moreover, we find that the hyperuniform structures, which are characterized by an anomalous suppression of volume-fraction fluctuations, tend to have lower values of the permeability, including MRJ sphere packings, quantizer configurations, and BCC sphere packings.