Deformation of interacting gas bubbles in liquid under acoustic excitation

A.A. Aganin^∗, A.I. Davletshin^∗∗

Institute of Mechanics and Engineering, FRC Kazan Scientific Center, Russian Academy of Sciences, Kazan, 420111 Russia

E-mail: ^∗aganin@kfti.knc.ru, ^∗∗anas.davletshin@gmail.com

Received April 17, 2018

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Abstract

The deformation of interacting bubbles in liquid in the pressure antinode of a standing ultrasound wave where the pressure varies harmonically has been studied. One of the simplest non-axisymmetric configurations – comprising five bubbles located on two orthogonal straight lines – has been considered. One of the bubbles is at the point of intersection of those lines, the others are equally distant from it. We have applied a mathematical model, a set of the ordinary differential equations of the second order in the bubble radii, the bubble center positionvectors, and the vectors characterizing small deviations of the shape of the bubbles from the spherical one in the form of spherical harmonics. The results show that the shape of the central bubble in the considered configuration turns out to be essentially spheroidal (with the axis of the spheroidal non-sphericity being orthogonal to the plane containing the bubble centers), which is quite surprising, because the spheroidal non-sphericity is typical of a bubble located between two other bubbles, whereas in the case under study with four neighboring bubbles one may expect that the maximum non-sphericity level will be due to the deformations in the form of harmonics defined by the associated Legendre polynomial of the fourth order.

Keywords: bubble dynamics, radial bubble oscillations, bubble interaction, small bubble deformations, bubble translations, acoustic excitation, spherical function method, interacting bubble equations

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For citation: Aganin A.A., Davletshin A.I. Deformation of interacting gas bubbles in liquid under acoustic excitation. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2018, vol. 160, no. 4, pp. 657–669. (In Russian)

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