Young's law for a nonlocal isoperimetric model of charged capillarity droplets

TL;DR

This paper investigates a mathematical model of charged liquid droplets on surfaces, proving that Young's law for contact angles holds under certain conditions in a nonlocal isoperimetric setting.

Contribution

It establishes the validity of Young's law for contact angles in a nonlocal charged droplet model with Coulomb interactions in 2D for small charges.

Findings

Young's law holds for small charges in the model.

The model captures equilibrium configurations of charged droplets.

The study provides a rigorous mathematical foundation for contact angle behavior.

Abstract

We study a variational problem modeling equilibrium configurations of charged liquid droplets resting on a surface under a convexity constraint. In the two-dimensional case with Coulomb interactions, we establish the validity of Young's law for the contact angle for small enough charges.