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