Stationary Soap Film Bridge Formed by a Small Electrostatic Force

TL;DR

This paper investigates how small electrostatic forces affect the shape and stability of soap film bridges, using two mathematical models to analyze stationary solutions and their sensitivity to force variations.

Contribution

It introduces two models for electrostatically influenced soap film bridges and analyzes the existence, stability, and shape dependence of stationary solutions under small forces.

Findings

Stationary solutions exist for small electrostatic forces.

Stability of solutions depends on force magnitude.

Shape of the soap film bridge varies with force strength.

Abstract

We consider two models, a free boundary problem and a simplification thereof, which describe a soap film bridge subjected to an electrostatic force. For both models, we construct stationary solutions if the force is small, analyse their stability and examine how their shape is influenced by small changes in the strength of the force.