Drying of capillary porous media with a stabilized front in two dimensions

We study a two-dimensional model of drying of capillary porous media when gravity or viscous forces lead to the formation of a stabilized front. When gravity forces stabilize the front, the mean front width, defined as the mean perpendicular distance between the front’s most advanced and least advanced points, is found theoretically to scale with the Bond number B as $B^{-1+(1+\beta )/(1+\nu )},$ where β is the percolation probability exponent and $\nu$ is the correlation length exponent. This scaling is confirmed numerically and is consistent with the experimental results of Shaw [Phys. Rev. Lett. 59, 1671 (1987)]. The global mass transfer coefficient of the front is studied numerically. To this end, we study the position $z_c-\delta$ of the equivalent smooth line leading to the same evaporation flux as the front. In the transient case, $z_c-\delta$ is found to scale with the Bond number B as $B^{-0.63}.$ In the stationary case, i.e., when the front reaches a stationary position within the medium, it is found that $z_c-\delta \approx \sigma$ where σ is the standard deviation of the positions of the points forming the front around its mean position $z_c.$ These results are exploited to study the evaporation flux when viscous effects stabilize the front. In particular, we discuss the possibility of nontrivial behaviors, i.e., drying rates not scaling as $1/\sqrt{t}$ for drying under constant external conditions.