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Droplet motion on inclined heterogeneous substrates

Published online by Cambridge University Press:  14 May 2013

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

We consider the static and dynamic behaviour of two-dimensional droplets on inclined heterogeneous substrates. We utilize an evolution equation for the droplet thickness based on the long-wave approximation of the Stokes equations in the presence of slip. Through a singular perturbation procedure, evolution equations for the location of the two moving fronts are obtained under the assumption of quasi-static dynamics. The deduced equations, which are verified by direct comparisons with numerical solutions to the governing equation, are scrutinized in a variety of dynamic and equilibrium settings. For example, we demonstrate the possibility for stick–slip dynamics, substrate-induced hysteresis, the uphill motion of the droplet for sufficiently strong chemical gradients and the existence of a critical inclination angle beyond which the droplet can no longer be supported at equilibrium. Where possible, analytical expressions are obtained for various quantities of interest, which are also verified by appropriate numerical experiments.

JFM classification

Interfacial Flows (free surface): Contact lines Drops and Bubbles: Drops Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 725 , 25 June 2013 , pp. 462 - 491
Copyright
©2013 Cambridge University Press 

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