A proof of the invariance of the contact angle in Electrowetting

TL;DR

This paper provides a rigorous mathematical proof that the contact angle in electrowetting remains invariant when an electrified droplet spreads on a solid surface, based on energy minimization principles.

Contribution

It introduces a variational approach to prove the invariance of the contact angle in electrowetting, a result previously assumed but not rigorously established.

Findings

Proves the invariance of contact angle in electrowetting.

Uses variational methods and energy minimization.

Derives necessary conditions for equilibrium shape of the droplet.

Abstract

We prove the invariance of the contact angle in liquid-solid wetting phenomena : an electrified droplet is spreading on a solid surface. The drop is minimizing its energy. We express the differential of this energy with respect to the shape of the drop and deduce necessary conditions for optimality . By variational method, using well-chosen test functions, we obtain the main result about the contact angle between the drop and the solid.