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 ${\mathcal{H}}^{d-1}$-a.e. along the contact line at every time.

arXiv commentBased 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