Source-like solution for radial imbibition into a homogeneous semi-infinite porous medium

Details Source-like solution for radial imbibition into a homogeneous semi-infinite porous medium Source-like solution for radial imbibition into a homogeneous semi-infinite porous medium

2012-02-16

arxiv.org/abs/1202.3818v1

Physics

Fluid Dynamics

work first presented at APS-DFD 2011 conference

Scientific paper

10.1021/la204474f

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 \approx t^(1/3). This cube-root law for the long-time dynamics is confirmed by experiments using a packed cell of glass microspheres with average diameter of 42 {\mu}m. This result complements the classical one-dimensional imbibition result where the imbibition length l \approx t^(1/2), and studies in axisymmetric porous cones with small opening angles where l \approx t^(1/4) at long times.

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