Superfast non-linear diffusion: capillary transport in particulate porous media

Lukyanov, A.V., Sushchikh, M.M., Baines, M.J. and Theofanous, T.G. (2012) Superfast non-linear diffusion: capillary transport in particulate porous media. Physical Review Letters, 109 (21). 214501. ISSN 0031-9007 doi: 10.1103/PhysRevLett.109.214501

Abstract/Summary

The migration of liquids in porous media, such as sand, has been commonly considered at high saturation levels with liquid pathways at pore dimensions. In this letter we reveal a low saturation regime observed in our experiments with droplets of extremely low volatility liquids deposited on sand. In this regime the liquid is mostly found within the grain surface roughness and in the capillary bridges formed at the contacts between the grains. The bridges act as variable-volume reservoirs and the flow is driven by the capillary pressure arising at the wetting front according to the roughness length scales. We propose that this migration (spreading) is the result of interplay between the bridge volume adjustment to this pressure distribution and viscous losses of a creeping flow within the roughness. The net macroscopic result is a special case of non-linear diffusion described by a superfast diffusion equation (SFDE) for saturation with distinctive mathematical character. We obtain solutions to a moving boundary problem defined by SFDE that robustly convey a time power law of spreading as seen in our experiments.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/29798
Item Type	Article
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	American Physical Society
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