Droplet motion with contact-line friction

long-time asymptotics in complete wetting

Journal article (2023)

Authors

Lorenzo Giacomelli Sapienza University of Rome
M.V. Gnann Mathematical Physics - EEMCS
Dirk Peschka Weierstraß-Institut
Research Group
Mathematical Physics (EEMCS) (TU Delft)
Copyright: © 2023 Lorenzo Giacomelli, M.V. Gnann, Dirk Peschka
DOI: https://doi.org/10.1098/rspa.2023.0090
Self-similar solutions Thin films Dynamic contact angle
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Published Date

2023

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Mathematical Physics

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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