Radiation forces between two bubbles in a compressible liquid

Abstract

The expression for the interaction force exerted by a sound field between two gas bubbles, allowing for the compressibility of the surrounding liquid, is derived. The bubble radii are considered to be small compared to the distance l between the equilibrium centers of the bubbles and the wavelength λ of sound, while the ratio of l to λ is assumed to be arbitrary. For an incompressible liquid, the interaction force, usually called the mutual or secondary Bjerknes force, is known to be inversely proportional to l2. It is found that when it is taken into account, the compressibility of the liquid gives rise to two long-range terms inversely proportional to l; one of these, like the Bjerknes force, is directed along the line joining the centers of the bubbles, and the other is in the direction of the gradient of an incident field. The refined expression of the interaction force is used for studies of the relative motion of the two bubbles, resulting from their radiative interaction, in a plane traveling wave and a plane standing wave. It is shown that the long-range terms can cause the bubbles to form stable bound pairs with a fixed separation between the bubbles.

Acoustic radiation interparticle forces in a compressible fluid

“…Comparison of (2.68) and (2.69) with the corresponding equations obtained in Doinikov & Zavtrak (1997) shows that they are in perfect agreement. Furthermore, in the limit k → 0 both (2.68) and (2.69) reduce to…”

“…The limit analogous to that considered here was first investigated by Doinikov & Zavtrak (1997) for the case of two-bubble interaction. In order to show that the new theory recovers their results, we also apply (2.60)-(2.62) to the case of two bubbles.…”

“…Their results give an explanation for stable bubble clusters, 'bubble grapes', which were observed experimentally by Kobelev, Ostrovskii & Sutin (1979), and also predict a number of new interesting effects. For the case of two bubbles, the situation has also been considered where the separation distance, remaining large compared with the bubble radii, is comparable with or more than the wavelength of sound (Zheng & Apfel 1995;Doinikov & Zavtrak 1997). Under such conditions, the calculation of the interaction force requires allowing for the compressibility of the host fluid.…”

Coupled pulsation and translation of two gas bubbles in a liquid

“…Subsequent work of Takahira, Fujikawa & Akamatsu (1989) reports a difference between bubble responses to resonances caused by primary and secondary Bjerknes forces. Compressibility of the surrounding liquid also gives rise to two long-range forces (Doinikov & Zavtrak 1997) that become important when the wavelength of the incident sound field is so short as to be comparable to the bubble separation distance. These forces act along the direction of the line of centres and of the gradient of the incident acoustic field, and they can combine to create stable bound pairs in which the bubbles maintain a fixed separation distance.…”

Interactions in an Acoustic World: Dumb Hole

“…The bubbles are able to interact each other in the presence of the acoustic waves, and therefore in the presence of the waves background of the acoustics world. Then a further development of the papers [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] can be done starting from this issue.…”