This article has an erratum: [erratum]

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 http://dx.doi.org/10.1209/0295-5075/87/54002
Published online 18 September 2009
EPL, 87 (2009) 54002
DOI: 10.1209/0295-5075/87/54002

Anomalous diffusion on clusters in steady-state two-phase flow in porous media in two dimensions

G. Tørå1, T. Ramstad2 and A. Hansen1

1   Department of Physics, Norwegian University of Science and Technology - N-7491 Trondheim, Norway
2   Numerical Rocks AS - Stiklestadveien 1, N-7041 Trondheim, Norway

glennt@ntnu.no
thomas@numericalrocks.com
Alex.Hansen@ntnu.no

received 13 November 2008; accepted in final form 19 August 2009; published September 2009
published online 18 September 2009

Abstract
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, $d_{{\rm rw}\parallel }$ = 2.35 $\pm$ 0.05 in the average flow direction and $d_{{\rm rw}\perp }$ = 3.51 $\pm$ 0.05 in the perpendicular direction. We determine the conductivity exponents to be $\mu _{\parallel }$ = 1.6 $\pm$ 0.2 and $\mu _{\perp }$ = 1.25 $\pm$ 0.1, respectively. The high-frequency scaling exponents of the AC conductivity we find to be $\eta _{\parallel }$ =0. 37 $\pm$ 0.1 and $\eta _{\perp }$ = 0.36 $\pm$ 0.1, respectively.

PACS
47.56.+r - Flows through porous media.
64.60.ah - Percolation.
07.05.Tp - Computer modeling and simulation.

© EPLA 2009