A Geometric Diffuse-Interface Method for Droplet Spreading
|Title:||A Geometric Diffuse-Interface Method for Droplet Spreading||Authors:||Holm, Darryl D.; Ó Náraigh, Lennon; Tronci, Cesare||Permanent link:||http://hdl.handle.net/10197/11584||Date:||Jan-2020||Online since:||2020-09-22T14:34:21Z||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.||Funding Details:||European Commission Horizon 2020||metadata.dc.description.othersponsorship:||EPSRC Standard
Alexander von Humboldt Foundation
German Federal Ministry for Education and Research
|Type of material:||Journal Article||Publisher:||Royal Society||Journal:||Proceedings of the Royal Society A||Volume:||476||Issue:||2233||Copyright (published version):||2020 the Authors||Keywords:||Contact-line flows; Diffuse-interface methods; Geometric mechanics||DOI:||10.1098/rspa.2019.0222||Language:||en||Status of Item:||Peer reviewed|
|Appears in Collections:||Mathematics and Statistics Research Collection|
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