Deformation and interaction of cylindrical bubbles.

Abstract

Experiments performed by Sankin et al. [Phys. Rev. Lett. 105, 078101 (2010)] demonstrate shape deformation of two coupled laser-generated bubbles confined between parallel surfaces. Due to their confinement, their motion is predominantly two-dimensional. It is known that any change in the volume of a cylindrical bubble in an unbounded incompressible fluid is prohibited because the effective mass loading is infinite. The natural frequency of a cylindrical bubble in its pure radial pulsation mode is correspondingly zero, and it becomes finite only if the surrounding fluid is either compressible or of limited extent. Because the higher-order modes of an oscillating cylindrical bubble involve no change in volume, their natural frequencies remain finite in an infinite incompressible fluid. Using the approach developed to model shape deformation of two coupled spherical bubbles [Kurihara et al., J. Acoust. Soc. Am. 127, 1760 (2010)] we obtained a set of coupled second-order ordinary differential equations in two dimensions describing the pulsation, translation, and deformation of coupled cylindrical bubbles. The presentation will focus on the deformation of a single cylindrical bubble, and the interaction and deformation of two cylindrical bubbles. [Work supported by NIH Grant Nos. DK070618 and EB011603.]