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Updated: May 16, 2026
08:01
The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Superfast nonlinear diffusion: capillary transport in particulate porous media
A V Lukyanov1, M M Sushchikh, M J Baines
1Department of Mathematics and Statistics, University of Reading, Reading RG6 6AX, United Kingdom.
Physical Review Letters
|December 11, 2012
Summary
This study reveals a new low saturation liquid migration regime in sand, driven by capillary bridges and surface roughness. This process follows a superfast diffusion equation, explaining observed time-dependent spreading.
Area of Science:
- Physics
- Geology
- Materials Science
Background:
- Liquid migration in porous media is typically studied at high saturation levels.
- Understanding low saturation liquid behavior in granular materials is crucial for various applications.
Purpose of the Study:
- To investigate and characterize liquid migration in porous media at extremely low saturation levels.
- To identify the governing mechanisms and mathematical description of this low saturation regime.
Main Methods:
- Experimental observation of droplet migration on sand with extremely low volatility liquids.
- Analysis of liquid distribution within grain surface roughness and capillary bridges.
- Mathematical modeling using a superfast diffusion equation for saturation.
Main Results:
- A distinct low saturation regime was identified where liquid resides in grain surface roughness and capillary bridges.
- Capillary bridges act as reservoirs, with flow driven by capillary pressure related to roughness scales.
- The spreading dynamics were accurately described by a superfast diffusion equation, exhibiting a time power law.
Conclusions:
- Liquid migration at low saturation in porous media is governed by surface roughness and capillary bridge dynamics.
- A superfast diffusion equation effectively models this nonlinear diffusion process.
- The findings provide new insights into fluid transport in granular materials under specific conditions.
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