The expression for the mutual interaction force between two pulsating gas bubbles immersed in an incompressible and inviscid fluid is derived assuming that the distance between the bubbles is comparable to their sizes. The results of numerical calculations for air bubbles in water are presented. They show that at small distances between the bubbles the interaction force is substantially different from that given by Bjerknes’ theory [Fields of Force (Columbia University Press, New York, 1906)] in which the separation distance between the bubbles is assumed to be large in comparison with the bubble sizes. The discrepancy seems to result from the effect of multiple scattering which is no longer negligible when the bubbles come close to each other. The present study enables one to understand the mechanism of the formation of the stable bubble clusters (‘‘bubble grapes’’) observed experimentally by Kobelev et al. [Pis’ma Zh. Eksp. Teor. Fiz. 30, 423 (1979)].

A suggestion is advanced that the stable bubble clusters observed by Marston et al. [Bubble Dynamics and Interface Phenomena, edited by J. R. Blake et al. (Kluwer Academic, Dordrecht, 1994), pp. 343–353] in an ultrasonic field are due to the radiative interaction forces of the bubbles, which change from attraction to repulsion when the distances between the bubbles become comparable with their sizes. This reversal is predicted by a theory developed in a previous paper by the authors [Phys. Fluids 7, 1923–1930 (1995)].

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.

A new simple scheme of an acoustical laser with mechanical pumping is suggested. In accordance with this scheme the pumping is created by a piezoelectric emitter of the piston type. The liquid with dispersed particles ͑gas bubbles͒ plays the role of an active medium. Phase bunching of the particles is realized by acoustical radiation forces. Generation conditions for this acoustical laser are evaluated. It is shown that two types of losses must be overcome for the beginning of the generation. The first type results from the energy dissipation in the active medium and the second one is caused by radiation losses at the boundaries of the resonator.

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