Paul E. Barbone
Dept. of Aerospace and Mech. Eng., 110 Cummington St., Boston Univ., Boston, MA 02215
The Rayleigh--Plesset equation describes the oscillations of a spherical bubble wall under the assumption that the fluid surrounding the bubble is incompressible. Many modifications of this equation have been proposed to incorporate slight fluid compressibility, and though different in form, they are asymptotically equivalent. The different forms of the equations, however, reveal remarkably different properties. In some forms of the modified Rayleigh--Plesset equation, for example, spurious unstable solutions are present while in other cases they are not. Here, physically motivated restrictions on the form of the modified Rayleigh--Plesset equation are discussed. These restrictions are discussed in the context of causality requirements and higher-order corrections to the modified Rayleigh--Plesset equation.