Abstract
We study the forced fluid invasion of an air-filled model porous medium at constant flow rate, in 1+1 dimensions, both experimentally and theoretically. We focus on the nonlocal character of the interface dynamics, due to liquid conservation, and its effect on the scaling properties of the interface upon roughening. Specifically, we study the limit of large flow rates and weak capillary forces. Our theory predicts a roughening behaviour characterized at short times by a growth exponent β1 = 5/6, a roughness exponent α1 = 5/2, and a dynamic exponent z1 = 3, and by β2 = 1/2, α2 = 1/2, and z2 = 1 at long times, before saturation. This theoretical prediction is in good agreement with the experiments at long times. The ensemble of experiments, theory, and simulations provides evidence for a new universality class of interface roughening in 1+1 dimensions.