We describe the imbibition process from a point source into a homogeneous semi-infinite porous material. When body forces are negligible, the advance of the wetting front is driven by capillary pressure and resisted by viscous forces. With the assumption that the wetting front assumes a hemispherical shape, our analytical results show that the absorbed volume flow rate is approximately constant with respect to time, and that the radius of the wetting evolves in time as r ¡Ö t1/3.

Junfeng Xiao, Howard A. Stone and Daniel Attinger. Source-like Solution for Radial Imbibition into a Homogeneous Semi-infinite Porous Medium. Langmuir, 2012, 28 (9), 4208-4212.