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

¹ Simulation of Physical Systems Group, Department of Physics, Universidad Nacional de Colombia, Carrera 30 No. 45-03, Ed. 404, Of. 348, Bogota D.C., Colombia
² Centro de Física Teórica e Computacional, Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, P-1749-016 Lisboa, Portugal

^* e-mail: macardenasb@unal.edu.co
^** e-mail: jdmunozc@unal.edu.co
^*** e-mail: nmaraujo@fc.ul.pt

Published online: 30 June 2017

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 λ of the capillary bridges among grains. Low λs generate a disconnect structure, with small clusters everywhere. On the contrary, for high λ, 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 λ on a granular media of monodisperse spheres in a random close packing. We determine both the percolating threshold λ_c = (0.049 ± 0.004)R (with R the radius of the granular spheres), and the critical exponent of the correlation length v = 0.830 ± 0.051, suggesting that the percolation transition falls into the universality class of ordinary percolation.