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

Published online by Cambridge University Press:  07 August 2014

Nikos Savva  and
Serafim Kalliadasis
Nikos Savva
Affiliation:
School of Mathematics, Cardiff University, Cardiff CF24 4AG, UK Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK
Serafim Kalliadasis*
Affiliation:
Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK
*
†Email address for correspondence: s.kalliadasis@imperial.ac.uk
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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.

JFM classification

Interfacial Flows (free surface): Contact lines Drops and Bubbles: Drops Low-Reynolds-number flows: Lubrication theory

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Type
Papers
Information
Journal of Fluid Mechanics , Volume 754 , 10 September 2014 , pp. 515 - 549
Copyright
© 2014 Cambridge University Press 

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