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A geometric diffuse-interface method for droplet spreading.

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.

SUBMITTER: Holm DD

PROVIDER: S-EPMC7016561 | biostudies-literature | 2020 Jan

REPOSITORIES: biostudies-literature

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A geometric diffuse-interface method for droplet spreading.

Holm Darryl D DD Náraigh Lennon Ó LÓ Tronci Cesare C

Proceedings. Mathematical, physical, and engineering sciences 20200108 2233

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 fo ...[more]

PMID: 32082051

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