Linear oscillations of a compressible hemispherical bubble on a solid substrate

Abstract

The linear natural and forced oscillations of a compressible hemispherical bubble on a solid substrate are under theoretical consideration. The contact line dynamics is taken into account by application of the Hocking condition, which eventually leads to nontrivial 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. A double resonance, where independent of the Hocking parameter, an unbounded growth of the amplitude occurs, is detected. The limiting case of weakly compressible bubble is studied. The general criterion identifying whether the compressibility of a bubble can be neglected is obtained.