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

TL;DR

This paper investigates the linear oscillations of a gas pocket on a submerged solid surface under acoustic excitation, deriving semi-analytical formulas for resonance frequency, damping, and interface shape considering potential and Stokes flows.

Contribution

It introduces semi-analytical expressions for gas pocket oscillations, accounting for two flow regimes and key dimensionless parameters, advancing understanding of their dynamic behavior.

Findings

Resonance frequency increases with gas pressure and decreases in surface tension.

Oscillation characteristics depend on gas stiffness, surface tension, and viscous effects.

Asymptotic resonance frequency reached at high gas pressure or low surface tension.

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.