Interface roughening in Hele-Shaw flows with quenched disorder: Experimental and theoretical results

We study the forced fluid invasion of an air-filled model porous medium at constant ow rate, in 1 + 1 dimensions, both experimentally and theoreticall y. We focus on the nonlocal character of the interface dynamics, due to liq uid conservation, and its effect on the scaling properties of the interface upon roughening. Specifically, we study the limit of large ow rates and we ak capillary forces. Our theory predicts a roughening behaviour characteriz ed at short times by a growth exponent beta (1) = 5/6, a roughness exponent alpha (1) = 5/2, and a dynamic exponent z(1) = 3, and by beta (2) = 1/2, a lpha (2) = 1/2, and z(2) = 1 at long times, before saturation. This theoret ical prediction is in good agreement with the experiments at long times. Th e ensemble of experiments, theory, and simulations provides evidence for a new universality class of interface roughening in 1 + 1 dimensions.