We study experimentally the case of steady-state simultaneous two-phase flow in a quasi-two-dimensional porous media. The dynamics is dominated by the interplay between a viscous pressure field from the wetting fluid and bubble transport of a less viscous, nonwetting phase. In contrast with more studied displacement front systems, steady-state flow is in equilibrium, statistically speaking. The corresponding theoretical simplicity allows us to explain a data collapse in the cluster size distribution as well as the relation $|\nabla P|\propto \sqrt{\mathrm{Ca}}$ between the pressure gradient in the system and the capillary number.

• Received 16 October 2008

DOI:https://doi.org/10.1103/PhysRevLett.102.074502