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Dynamics of droplets on cones: self-propulsion due to curvature gradients

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Abstract

We study the dynamics of droplets driven by a gradient of curvature, as may be achieved by placing a drop on the surface of a cone. The curvature gradient induces a pressure gradient within the drop, which in turn leads to spontaneous propulsion of the droplet. To investigate the resulting driving force we perform a series of experiments in which we track a droplet's displacement, s, from the apex of a cone whose surface is treated to exhibit near-zero pinning effects. We find an st1/4 scaling at sufficiently late times t. To shed light upon these dynamics, we perform an asymptotic calculation of the equilibrium shape of a droplet on a weakly curved cylinder, deriving the curvature-induced force responsible for its propulsion. By balancing this driving force with viscous dissipation, we recover a differential equation for the droplet displacement, whose predictions are found to be in good agreement with our experimental results.

Graphical abstract: Dynamics of droplets on cones: self-propulsion due to curvature gradients

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Publication details

The article was received on 12 Aug 2019, accepted on 12 Nov 2019 and first published on 14 Nov 2019


Article type: Paper
DOI: 10.1039/C9SM01635J
Soft Matter, 2019, Advance Article

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    Dynamics of droplets on cones: self-propulsion due to curvature gradients

    J. McCarthy, D. Vella and A. A. Castrejón-Pita, Soft Matter, 2019, Advance Article , DOI: 10.1039/C9SM01635J

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