Percolation Theory for Flow in Porous Media
I came across percolation theory when studying battery separator materials. Linked below is a book titled “Percolation Theory for Flow in Porous Media” by Allen Hunt, Robert Ewing, and Behzad Ghanbarian. As defined by the book, “Percolation theory describes emergent properties related to the connectivity of large numbers of objects. These objects typically have some spatial extent, and their spatial
relationships are relevant and statistically prescribed.” The book says that the question of whether a fluid can flow through a porous material is largely about the connectivity of the pores. Unless there is a path of connected pores that spans the whole sample, fluids will not be able to flow through the material. Percolation theory can be applied to soils, textiles, building materials, conductive materials and much more.
While we have not discussed percolation theory in Networks, it is highly dependent on graph theory and network theory (we have discussed graph connectivity extensively). We defined a strongly connected component as a set of nodes S such that each node in S can reach each other node in S respecting the directions of edges, and it is not part of any larger set with this property. Basic percolation theory as applied to a porous material says that fluid can flow through a material only if there is a strongly connected component (nodes = pores) where at least one pore connects to the outer surface on one side of the sample, and another pore connects to the opposite outer surface of the sample.
https://link.springer.com/content/pdf/10.1007%2F978-3-319-03771-4.pdf
Lecture Notes in Physics Volume 880