On the geometry of rate independent droplet evolution
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 -a.e. along the contact line at every time.
Keywords
Cite
@article{arxiv.2310.03656,
title = {On the geometry of rate independent droplet evolution},
author = {William M Feldman and Inwon C. Kim and Norbert Požár},
journal= {arXiv preprint arXiv:2310.03656},
year = {2024}
}
Comments
Based on readers' feedback we have split our work, whose original version can be found at arXiv:2310.03656v1, into two independent parts containing all the results of the original paper. The other part of the paper (on obstacle solutions) has appeared as a new separate posting at arXiv:2410.06931