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

Lorenzo Giacomelli, Manuel V. Gnann, Dirk Peschka*

*Corresponding author for this work

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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 languageEnglish
Article number20230090
Number of pages19
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2274
Publication statusPublished - 2023

Bibliographical note

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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


  • dynamic contact angle
  • self-similar solutions
  • thin films


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