Paul E. Barbone
Dept. of Aerospace and Mech. Eng., Boston Univ., 110 Cummington St., Boston, MA 02215
Following a method similar to that used to obtain the standard Rayleigh--Plesset equation, equations are derived describing the volume oscillations of two interacting spherical bubbles, whose centers are assumed to be a large distance (relative to the equilibrium radii of the bubbles) apart in an infinite fluid. Although the bubbles are initially assumed to be fixed, these approximate equations also describe the movement of the bubble centers. First, the natural frequencies of the two-bubble system are obtained via linearization. Then, for bubbles with the same equilibrium radii, the nonlinear stability of the symmetric and antisymmetric modes is studied both analytically and numerically. The response of the two-bubble system to a time-periodic pressure field is also studied. Finally, the equations for the two-bubble system are generalized to those describing an n-bubble system, and an estimate is obtained for the lowest resonant frequency of the n-bubble cloud.