Radiation forces between two bubbles in a compressible liquid

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 lambda of sound, while the ratio of l to lambda 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 l(2). It is found that when it is taken into account, the compressibility of the liquid gives rise to two Icing-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. (C) 1997 Acoustical Society of America.