| Issue |
EPL
Volume 87, Number 5, September 2009
|
|
|---|---|---|
| Article Number | 54002 | |
| Number of page(s) | 6 | |
| Section | Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics | |
| DOI | https://doi.org/10.1209/0295-5075/87/54002 | |
| Published online | 18 September 2009 | |
Anomalous diffusion on clusters in steady-state two-phase flow in porous media in two dimensions
1
Department of Physics, Norwegian University of Science and Technology - N-7491 Trondheim, Norway
2
Numerical Rocks AS - Stiklestadveien 1, N-7041 Trondheim, Norway
Corresponding authors: glennt@ntnu.no thomas@numericalrocks.com Alex.Hansen@ntnu.no
Received:
13
November
2008
Accepted:
19
August
2009
We study diffusion processes on clusters of non-wetting fluid dispersed in a wetting one flowing in a two-dimensional porous medium under steady-state conditions using a numerical model. At the critical saturation and capillary number of 10-5, where the cluster size distribution follows a power law, we find anomalous diffusion characterized by two critical exponents, 
= 2.35 ± 0.05 in the average flow direction and 
= 3.51 ± 0.05 in the perpendicular direction. We determine the conductivity exponents to be 
= 1.6 ± 0.2 and 
= 1.25 ± 0.1, respectively. The high-frequency scaling exponents of the AC conductivity we find to be 
=0. 37 ± 0.1 and 
= 0.36 ± 0.1, respectively.
PACS: 47.56.+r – Flows through porous media / 64.60.ah – Percolation / 07.05.Tp – Computer modeling and simulation
© EPLA, 2009
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