Droplet motion with contact-line friction: long-time asymptotics in complete wetting

Lorenzo Giacomelli; Manuel V. Gnann; Dirk Peschka

doi:10.1098/rspa.2023.0090

Droplet motion with contact-line friction: long-time asymptotics in complete wetting

Lorenzo Giacomelli, Manuel V. Gnann, Dirk Peschka^*

^*Corresponding author for this work

Mathematical Physics

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Abstract

We consider the thin-film equation for a class of free boundary conditions modelling friction at the contact line, as introduced by E and Ren. Our analysis focuses on formal long-time asymptotics of solutions in the perfect wetting regime. In particular, through the analysis of quasi-self-similar solutions, we characterize the profile and the spreading rate of solutions depending on the strength of friction at the contact line, as well as their (global or local) corrections, which are due to the dynamical nature of the free boundary conditions. These results are complemented with full transient numerical solutions of the free boundary problem.

Original language	English
Article number	20230090
Number of pages	19
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	479
Issue number	2274
DOIs	https://doi.org/10.1098/rspa.2023.0090
Publication status	Published - 2023

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Funding

M.V.G. was partially supported by the Deutsche Forschungsgemeinschaft (DFG) under project no. 334362478. D.P. acknowledges the financial support within the DFG-Priority Programme 2171 by project no. 422792530. L.G. acknowledges partial support by PRIN "Mathematics of active materials: From mechanobiology to smart devices" (2017KL4EF3). Acknowledgements

Keywords

dynamic contact angle
self-similar solutions
thin films

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10.1098/rspa.2023.0090

2302.03005 (1)Final published version, 4.9 MB

Cite this

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title = "Droplet motion with contact-line friction: long-time asymptotics in complete wetting",

abstract = "We consider the thin-film equation for a class of free boundary conditions modelling friction at the contact line, as introduced by E and Ren. Our analysis focuses on formal long-time asymptotics of solutions in the perfect wetting regime. In particular, through the analysis of quasi-self-similar solutions, we characterize the profile and the spreading rate of solutions depending on the strength of friction at the contact line, as well as their (global or local) corrections, which are due to the dynamical nature of the free boundary conditions. These results are complemented with full transient numerical solutions of the free boundary problem. ",

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Droplet motion with contact-line friction: long-time asymptotics in complete wetting

Abstract

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Keywords

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