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We examine theoretically the effects of random topographical substrates onthe motion of two-dimensional droplets via appropriate statistical approaches.Different random substrate families are represented as stationary randomfunctions. The variance of the droplet shift at both early times and in thelong-time limit is deduced and the droplet footprint is found to be a normalrandom variable at all times. It is shown that substrate roughness decreasesdroplet wetting, illustrating also the tendency of the droplet to slide withoutspreading as equilibrium is approached. Our theoretical predictions areverified by numerical experiments.

Two-dimensional droplet spreading over random topographical substrates