2024/09/27 by Lina Sophie Schmitz, Schmitz, Lina Sophie
Engineering · Materials Science · #35B35 #35Q99 #35R35 #42A32 #47J07 #Advanced Surface Polishing Techniques #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #High voltage insulation and dielectric phenomena #Mechanical stress and fatigue analysis
paper · pdf · doi:10.48550/arxiv.2409.18784
openalex publication_date 2024/09/27 · openalex created_date 2024/10/27 · openalex updated_date 2026/07/28
We analytically study a stationary free boundary problem describing a soap film bridge subjected to an electrostatic force. Starting from a cylinder that the soap film forms if its surface tension and the electrostatic force are perfectly balanced, we construct a local branch of stationary solutions. Then, we prove that there is a sharp threshold value for a characteristic model parameter at which the stability behaviour of this branch switches from stable to unstable. Finally, we show that the soap film deflects monotonically outwards if the strength of the electrostatic force is increased. Besides rigorous results, we also discuss a possible balancing effect of the electrostatic force.