On the geometry of rate independent droplet evolution

We introduce a toy model for rate-independent droplet motion on a surface with contact angle hysteresis based on the one-phase Bernoulli free boundary problem. We consider a notion of energy solutions and show existence by a minimizing movement scheme. The main result of the paper is on the PDE cond...

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Bibliographic Details
Published in:arXiv.org 2024-10
Main Authors: Feldman, William M, Kim, Inwon C, Požár, Norbert
Format: Article
Language:English
Subjects:
Contact angle
Droplets
Free boundaries
Online Access:Get full text
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Summary:We introduce a toy model for rate-independent droplet motion on a surface with contact angle hysteresis based on the one-phase Bernoulli free boundary problem. We consider a notion of energy solutions and show existence by a minimizing movement scheme. The main result of the paper is on the PDE conditions satisfied by general energy solutions: we show that the solutions satisfy the dynamic contact angle condition \(\mathcal{H}^{d-1}\)-a.e. along the contact line at every time.
ISSN:2331-8422