Abstract
We present a theoretical analysis of the capillary driven transport of liquid in porous media that undergoes a sudden expansion. The use of appropriate coordinates allows for exactly and analytically solving different cases in two and three dimensions. The time dependence of liquid front motion in an expanding porous media is shown to be different from the one-dimensional Lucas-Washburn [Lucas, Kolloid Z. 23, 15 (1918); Washburn, Phys. Rev. 17, 273 (1921)] results as well as from the solution for two- and three-dimensional circular expansions obtained by Hyv\"aluoma et al. [Phys. Rev. E 73, 036705 (2006)] and Xiao et al. [Langmuir 28, 4208 (2012)]. These cases appear as asymptotic limits of our solutions. We also observe that capillary flow in expanding three-dimensional porous materials exhibits a steady state solution for the bulk flow rate at the entrance of the expansion.
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