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

Abstract

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.

Description

Keywords

Integral tranforms, Gas liquids interfaces, Integral equations, Fourier analysis, Telecommunications engineering

Citation

Copyright 2012 Physics of Fluids. Recommended citation: Gelderblom, Hanneke, Aaldert G. Zijlstra, Leen Van Wijngaarden, and Andrea Prosperetti. "Oscillations of a gas pocket on a liquid-covered solid surface." Physics of fluids 24, no. 12 (2012): 122101. DOI: 10.1063/1.4769179 URL: https://aip.scitation.org/doi/abs/10.1063/1.4769179 Reproduced in accordance with the original publisher’s licensing terms and with permission from the author(s).