Oscillations of a gas pocket on a liquid-covered solid surface

• Published in: Physics of fluids (1994) Vol. 24; no. 12
• Main Authors: Gelderblom, Hanneke, Zijlstra, Aaldert G., van Wijngaarden, Leen, Prosperetti, Andrea
• Format: Journal Article
• Language: English
• Published: Melville, NY American Institute of Physics 01.12.2012
• Subjects: Asymptotic properties; Bubbles; Drops and bubbles; Exact sciences and technology; Fluid dynamics; Fluid flow; Fundamental areas of phenomenology (including applications); Hydrodynamic waves; Liquid phases; Nonhomogeneous flows; Oscillations; Physics; Stiffness; Surface tension; Unsteady; Gas liquid interface; Geometrical shape; Bubbles; Resonance frequency; Digital simulation; Gas solid interface; Oscillations; Modelling
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.4769179

The dynamic response of a gas bubble entrapped in a cavity on the surface of a submerged solid subject to an acoustic field is investigated in the linear approximation. We derive semi-analytical expressions for the resonance frequency, damping, and interface shape of the bubble. For the liquid phase, we consider two limit cases: potential flow and unsteady Stokes flow. The oscillation frequency and interface shape are found to depend on two dimensionless parameters: the ratio of the gas stiffness to the surface tension stiffness, and the Ohnesorge number, representing the relative importance of viscous forces. We perform a parametric study and show, among others, that an increase in the gas pressure or a decrease in the surface tension leads to an increase in the resonance frequency until an asymptotic value is reached.