Percolating length scales from topological persistence analysis of micro-CT images of porous materials

Abstract

Topological persistence is a powerful and general technique for characterizing the geometryand topology of data. Its theoretical foundations are over 15 years old and efficient computational algo-rithms are now available for the analysis of large digital images. We explain here how quantities derivedfrom topological persistence relate to other measurements on porous materials such as grain and pore-sizedistributions, connectivity numbers, and the critical radius of a percolating sphere. The connectionsbetween percolation and topological persistence are explored in detail using data obtained from micro-CTimages of spherical bead packings, unconsolidated sand packing, a variety of sandstones, and a limestone.We demonstrate how persistence information can be used to estimate the percolating sphere radius and tocharacterize the connectivity of the percolating cluster.