Percolation study for the capillary ascent of a liquid through a granular soil

TL;DR

This study investigates how the capillary rise of water in granular soil depends on the size of liquid bridges, identifying a percolation threshold and critical behavior that influence water movement in flood-prone construction areas.

Contribution

The paper introduces a geometric percolation model for capillary rise in granular media, determining the percolation threshold and critical exponent, linking it to the universality class of ordinary percolation.

Findings

Percolation threshold λ_c = 0.049 R

Critical exponent ν = 0.830

Transition belongs to ordinary percolation universality class

Abstract

Capillary rise plays a crucial role in the construction of road embankments in flood zones, where hydrophobic compounds are added to the soil to suppress the rising of water and avoid possible damage of the pavement. Water rises through liquid bridges, menisci and trimers, whose width and connectivity depends on the maximal half-length {\lambda} of the capillary bridges among grains. Low {\lambda} generate a disconnect structure, with small clusters everywhere. On the contrary, for high {\lambda}, create a percolating cluster of trimers and enclosed volumes that form a natural path for capillary rise. Hereby, we study the percolation transition of this geometric structure as a function of {\lambda} on a granular media of monodisperse spheres in a random close packing. We determine both the percolating threshold {\lambda}_{c} = (0.049 \pm 0.004)R (with R the radius of the granular spheres), and the critical exponent of the correlation length {\nu} = (0.830 \pm 0.051), suggesting that the percolation transition falls into the universality class of ordinary percolation.