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arXiv · 2310.03656

On the geometry of rate independent droplet evolution

William M Feldman·Inwon C. Kim·Norbert Požár
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Abstract

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.

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William M Feldman, Inwon C. Kim, Norbert Požár. 2023-10-05. On the geometry of rate independent droplet evolution. https://arxiv.org/abs/2310.03656

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