Percolation study for the capillary ascent of a liquid through a granular soil (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, trimers and enclosed volumes, and the void spaces among grains that could eventually take part of those capillary elements can eventually connect to form a path at disposal for capillary rise. The width and connectivity of that structure depends on the maximal half-length λ of a capillary bridge among the grains, which is a function of contact angle. Low λs generate a disconnect structure, with small clusters everywhere. On the contrary high λs 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 for a random dense packing of monodisperse spherical grains at volume fraction φ ' 0.63. We determined a percolation threshold for λc = (0.049 ± 0.004)R (with R the radius of the spheres), less than one fourth of the mean distance between neighbouring grains at that volume fraction. In addition, all critical exponents for the transition are in good agreement with those of size percolation in three dimensions, suggesting that the formation of trimers (i.e. the main components of the connected path for capillary rise) can be considered as randomly independent, a possible consequence of the random positions for the grains. The study combines capillary structures and percolation theory to investigate capillary rise through a granular medium. It constitutes an interesting novel approach and a new step in the understanding of this rich phenomenon