Acoustic interaction forces between two fluid spheres in an acoustic field

The acoustic interaction force between two fluid spheres in a plane acoustic wave field is investigated by calculating the radiation force due to the total acoustic field that includes the incident plane wave and the first- and second-order scattered fields of the objects. A general formula for the radiation force on one sphere is derived which shows the dependence on the resonant modes of the other. In the expression for the radiation force, there are cross terms that involve the primary plane wave and the scattered wave field. For two small bubbles, the result is reduced to the same as the Bjerknes force expression obtained by others under the approximation of long wavelength. Calculations are also done for the case when the primary wave is a standing-wave field.