### ASA 129th Meeting - Washington, DC - 1995 May 30 .. Jun 06

## 1aPA3. Acoustic response of interacting gas bubbles.

**Daniel Goldman
**

**
Paul E. Barbone
**

**
Ali Nadim
**

**
**
*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.