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Low-frequency vibrations of two-dimensional droplets on heterogeneous substrates

Savva, Nikos and Kalliadasis, Serafim 2014. Low-frequency vibrations of two-dimensional droplets on heterogeneous substrates. Journal of Fluid Mechanics 754 , pp. 515-549. 10.1017/jfm.2014.409

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Abstract

We present a theoretical investigation of the effects of low-frequency vibrations on the motion of two-dimensional droplets on heterogeneous substrates in the presence of gravity and substrate heterogeneities, both chemical and topographical. A combined analytical and numerical approach is undertaken, extending the work of Savva & Kalliadasis (J. Fluid Mech., vol. 725, 2013, pp. 462–491) on inclined heterogeneous substrates to include the effects of substrate vibrations. Via a matching procedure and under the quasi-static assumption, we obtain evolution equations for the moving fronts. These equations are then invoked in a wide variety of case studies. It is demonstrated that vertically vibrated horizontal ratcheted substrates can induce unidirectional motion. For inclined substrates, we focus on a number of qualitative aspects of the peculiar vibration-induced climbing of droplets reported in experiments by Brunet, Eggers & Deegan (Phys. Rev. Lett., vol. 99, 2007, art. 144501). We examine the effects of weak inertia on the dynamics, deduce analytical criteria for the uphill motion in the limit of weak gravitational and vibrational effects, and demonstrate that substrate heterogeneities may be utilised to enhance droplet transport.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Cambridge University Press
ISSN: 0022-1120
Date of First Compliant Deposit: 30 March 2016
Date of Acceptance: 14 July 2014
Last Modified: 05 Mar 2019 16:23
URI: http://orca.cf.ac.uk/id/eprint/63039

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