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A geometric diffuse-interface method for droplet spreading

Holm, Darryl D., Náraigh, Lennon Ó and Tronci, Cesare (2020) A geometric diffuse-interface method for droplet spreading Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 476 (2233).

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Abstract

This paper exploits the theory of geometric gradient flows to introduce an alternative regularization of the thin-film equation valid in the case of large-scale droplet spreading—the geometric diffuse-interface method. The method possesses some advantages when compared with the existing models of droplet spreading, namely the slip model, the precursor film method and the diffuse-interface model. These advantages are discussed and a case is made for using the geometric diffuse-interface method for the purpose of numerical simulations. The mathematical solutions of the geometric diffuse interface method are explored via such numerical simulations for the simple and well-studied case of large-scale droplet spreading for a perfectly wetting fluid— we demonstrate that the new method reproduces Tanner’s Law of droplet spreading via a simple and robust computational method, at a low computational cost. We discuss potential avenues for extending the method beyond the simple case of perfectly wetting fluids.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
NameEmailORCID
Holm, Darryl D.
Náraigh, Lennon Ó
Tronci, Cesarec.tronci@surrey.ac.uk
Date : 8 January 2020
Funders : EPSRC
DOI : 10.1098/rspa.2019.0222
OA Location : https://royalsocietypublishing.org/doi/full/10.1098/rspa.2019.0222
Grant Title : ‘Variational principles for stochastic parametrizations in geophysical fluid dynamics’
Copyright Disclaimer : © 2020 The Author(s) Published by the Royal Society. All rights reserved.
Depositing User : Rebecca Cooper
Date Deposited : 20 Jan 2020 09:40
Last Modified : 20 Jan 2020 10:51
URI: http://epubs.surrey.ac.uk/id/eprint/853342

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