Vapor bubble dynamics

The principles underlying the dynamics of a bubble filled with condensable vapor in a thermally conducting liquid are set out and the equations governing the radial motion of a spherical bubble in an unbounded liquid at a fixed temperature are derived. A linearized solution of these equations is then found, assuming harmonic acoustic drive. It is shown that the effective stiffness of the bubble is a complicated function of bubble radius and frequency; consequently it is possible for bubbles of two distinct sizes to resonate at the same frequency. Numerical values are presented for vapor bubbles in liquid Helium I, nitrogen, water, and for a liquid with the same effective thermal conductivity as liquid Helium II.