Flow of thin films on patterned surfaces: controlling the instability.

We present fully nonlinear time-dependent simulations of the gravity-driven flow of thin wetting liquid films. The computations of the flow on a homogeneous substrate show that the contact line, becomes unstable and develops a finger-like or sawtooth structure [Phys. Rev. Lett. 86, 632 (2001)]. These computations are extended to patterned surfaces, where surface heterogeneities are introduced in a controllable manner. We discuss the conditions that need to be satisfied so that surface properties lead to predictable pattern formation and controllable wetting of the substrate. These conditions are sensitive to the presence of noise which is introduced by random perturbations of the contact line. We analyze this sensitivity and suggest how the effects of noise can be minimized. Applications of these results to technologically relevant flows are discussed.