Capillary Filling with Randomly Coated Walls

The motion of an air-fluid interface through an irregularly coated capillary is studied by analyzing the Lucas-Washburn equation with inertia, viscosity and a random capillary force. Below a critical velocity, the front enters a strongly intermittent dynamic regime, as recently observed in experiments. Analytical estimates for the average asymptotic front trajectory and pinning length distribution are obtained, and a numerical procedure for predicting quantities of experimental interest is also illustrated.