Lateral drift of liquid droplets sliding down substrates with nonuniform dissipation

Abstract

Understanding and controlling the motion of liquid droplets is important both from a fundamental point of view and in many applications. In this work, we theoretically analyze the dynamics of a liquid droplet sliding down a ramp under the action of gravity. We show that when the dissipation (which we account for by means of an effective contact line viscosity) has a gradient in the direction orthogonal to gravity, the droplet, while sliding down, drifts laterally in the direction opposite to the dissipation gradient. We validate our analytical results, obtained in the limit of low Bond numbers, by a numerical solution of our model.