Symmetry Approach in the Evaluation of the Effect of Boundary Proximity on Oscillation of Gas Bubbles

Abstract

The purpose of the present review is to describe the effect of an interface between media with different mechanical properties on the acoustic response of a gas bubble. This is necessary to interpret sonar signals received from underwater gas seeps and mud volcanoes, as well as in the case of acoustic studies on the Arctic shelf where rising gas bubbles accumulate at the lower boundary of the ice cover. The ability to describe the dynamics of constrained bubble by analytical methods is related to the presence of internal symmetry in the governing equations. This leads to the presence of specific (toroidal and bi-spherical) coordinate systems in which the variables are separated. The existence of symmetry properties is possible only under certain conditions. In particular, the characteristic wavelength should be larger than the bubble size and the distance to an interface. The derived analytical solution allows us to determine how the natural frequency, radiation damping, and bubble shape depend on the distance to the boundary and the material parameters of contacting media.

Interferometric detection of hydrodynamic bubble–bubble interactions

“…More complex is the case of close inter-bubble distances, where the angular dependence in the description of the fluid velocity field cannot be neglected in the calculations. In the works by Maksimov (Maksimov & Yusupov 2016; Maksimov & Polovinka 2018), analytic expressions for this regime have been obtained by symmetry approaches (Maksimov 2018) involving the use of specific (bi-spherical) coordinate systems. In typical experiments, volume modes of micrometre-sized bubbles are excited by high-intensity ultrasound pulses, mimicking the set-ups used in applications.…”