Accessibility navigation

Superfast nonlinear diffusion: capillary transport in particulate porous media

Lukyanov, A. V., Shushchikh, M. M., Baines, M. J. and Thoephanus, T. G. (2012) Superfast nonlinear diffusion: capillary transport in particulate porous media. Physical Review Letters, 109 (21). pp. 214501-214504. ISSN 0031-9007

Full text not archived in this repository.

It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing.

To link to this item DOI: 10.1103/PhysRevLett.109.214501


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 nonlinear diffusion described by a superfast diffusion equation for saturation with distinctive mathematical character. We obtain solutions to a moving boundary problem defined by superfast diffusion equation that robustly convey a time power law of spreading as seen in our experiments.

Item Type:Article
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:68018
Publisher:American Physical Society

University Staff: Request a correction | Centaur Editors: Update this record

Page navigation