Труды Института механики им. Р.Р. Мавлютова

Aganin I.A., Davletshin A.I. Dynamics of two gas bubbles in liquid in an ultrasonic traveling wave. Proceedings of the Mavlyutov Institute of Mechanics. 12 (2017) 1. 33–39.

2017. Vol. 12. Issue 1, Pp. 33–39
URL: http://proc.uimech.org/uim2017.1.005
DOI: 10.21662/uim2017.1.005

Dynamics of two gas bubbles in liquid in an ultrasonic traveling wave

Aganin I.A., Davletshin A.I.

Institute of Mechanics and Engineering, Kazan

Abstract

The influence of the liquid viscosity and compressibility on the dynamics of two air bubbles (with equilibrium radii of 5 μm) in water at room conditions under the action of a plane ultrasonic wave traveling along the line of the bubble centers (the wavelength is 5000 μm, the amplitude is 0.3 bar) is studied. The initial distance between the centers of the bubbles is six bubble radii. A mathematical model is used, which is fourth-order accurate in terms of the ratio of the radius of the bubbles to the distance between them. It is shown that the spatial displacements of the bubbles are determined mainly by their hydrodynamic interaction. The influence of the liquid viscosity and compressibility is generally significant, and the viscosity affects much more. Without account of the liquid viscosity and compressibility, the bubbles collide with each other after the action of 4.5 running-wave lengths. With taking into account the liquid compressibility, the bubbles under the same action remain remote at a distance on the order of their equilibrium radii, while with additionally allowing for the liquid viscosity, their spacing is kept close to the initial one.

Keywords

dynamics of gas bubbles in liquid,
hydrodynamic interaction of bubbles,
ultrasonic traveling wave

Article outline

Purpose. Numerical study of the liquid viscosity and compressibility effects on the dynamics of two initially- identical spherical air bubbles in water under room conditions under the action of an ultrasonic plane wave running along the line of the bubble centers.

Methodology. A mathematical model of bubble dynamics is used, which is a system of second-order ordinary differential equations in the radii of the bubbles, the coordinates of their centers and the amplitudes of the deviations of their shape from the spherical one. The system of equations is solved numerically by a high-accurate Runge-Kutta method with an automatically chosen time step.

Findings. The spatial movements of bubbles are determined mainly by their hydrodynamic interaction. The influence of both the liquid viscosity and compressibility is significant (the viscosity affects much more) and manifests itself mainly in the spatial displacements and deformations of the bubble surfaces. Without account of the liquid viscosity and compressibility, the bubbles collide with each other after the action of 4.5 running-wave lengths. With taking into account the liquid compressibility, the bubbles under the same action remain remote at a distance on the order of their equilibrium radii, while with additionally allowing for the liquid viscosity, their spacing is kept close to the initial one.