Droplet motion on inclined heterogeneous substrates

Savva, Nikos ORCID: https://orcid.org/0000-0003-1549-3154 and Kalliadasis, Serafim 2013. Droplet motion on inclined heterogeneous substrates. Journal of Fluid Mechanics 725 , pp. 462-491. 10.1017/jfm.2013.201

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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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	contact lines; drops; thin films
Additional Information:	Pdf uploaded in accordance with publisher's policy at http://www.sherpa.ac.uk/romeo/issn/0022-1120/ (accessed 21/02/2014).
Publisher:	Cambridge University Press
ISSN:	0022-1120
Date of First Compliant Deposit:	30 March 2016
Last Modified:	04 May 2023 15:33
URI:	https://orca.cardiff.ac.uk/id/eprint/47381

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