Europhys. Lett.
Volume 71, Number 4, August 2005
Page(s) 583 - 589
Section Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics
Published online 22 July 2005
Europhys. Lett., 71 (4), pp. 583-589 (2005)
DOI: 10.1209/epl/i2005-10136-9

Influence of pore-scale disorder on viscous fingering during drainage

R. Toussaint1, 2, G. Løvoll1, Y. Méheust3, K. J. Måløy1 and J. Schmittbuhl2

1  Department of Physics, University of Oslo - PO Box 1048 Blindern N-0316 Oslo, Norway
2  Institut de Physique du Globe, UMR 7516 5 rue René Descartes, 67084 Strasbourg, France
3  Department of Physics, NTNU Trondheim - N-7491 Trondheim, Norway

received 18 April 2005; accepted 24 June 2005
published online 22 July 2005

We study viscous fingering during drainage experiments in linear Hele-Shaw cells filled with a random porous medium. The central zone of the cell is found to be statistically more occupied than the average, and to have a lateral width of 40% of the system width, irrespectively of the capillary number Ca. A crossover length $w_f\propto Ca^{-1}$ separates lower scales where the invader's fractal dimension $D\simeq 1.83$ is identical to capillary fingering, and larger scales where the dimension is found to be $D\simeq 1.53$. The lateral width and the large-scale dimension are lower than the results for Diffusion Limited Aggregation, but can be explained in terms of Dielectric Breakdown Model. Indeed, we show that when averaging over the quenched disorder in capillary thresholds, an effective law $v\propto(\nabla P)^2$ relates the average interface growth rate and the local pressure gradient.

47.20.Gv - Viscous instability.
47.54.+r - Pattern selection; pattern formation.
47.55.Mh - Flows through porous media.

© EDP Sciences 2005