Linear oscillations of a compressible hemispherical bubble on a solid substrate

TL;DR

This paper investigates the linear oscillations of a compressible hemispherical bubble on a solid surface, considering contact line dynamics and resonance phenomena, and provides criteria for when compressibility effects are negligible.

Contribution

It introduces a theoretical model for bubble oscillations including contact line dynamics and analyzes the effects of compressibility and resonance.

Findings

Resonance phenomena are pronounced for fixed contact line or contact angle.

A criterion for when bubble compressibility can be neglected is derived.

Weakly compressible bubble behavior is specifically analyzed.

Abstract

The linear natural and forced oscillations of a hemispherical bubble on a solid substrate are under theoretical consideration. The contact line dynamics is taken into account with the Hocking condition, which eventually leads to interaction of the shape and volume oscillations. Resonant phenomena, mostly pronounced for the bubble with the fixed contact line or with the fixed contact angle, are found out. The limiting case of weakly compressible bubble is studied. The general criterion identifying whether the compressibility of a bubble can be neglected is obtained.