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Spontaneous capillary propulsion of liquid droplets on substrates with nonuniform curvature
Phys. Rev. Fluids 3, 103601 – Published 5 October, 2018
DOI: https://doi.org/10.1103/PhysRevFluids.3.103601
Abstract
A liquid droplet spread on a solid substrate with nonuniform curvature, in the absence of pinning, spontaneously moves. By means of a perturbative scheme, we determine analytically the speed of the droplet and the total capillary force acting on it, by assuming that the only relevant dissipation mechanism is the contact line viscosity. Our solution holds for droplets small with respect to the capillary length and in the limit where the curvature of the substrate is small with respect to the curvature of the droplet. By means of a numerical solution, we validate our perturbative calculation and determine its limit of validity. Our theoretical results are in agreement with recent experimental data on the movement of submillimeter-sized water droplets on conical glass pipettes [Lv et al., Phys. Rev. Lett. 113, 026101 (2014)].
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