Motion transient collapse

Figure 9. Bubble radius and pressure transients of the water vapor inside the bubbles. The first maximum in pressure at 650 ps marks the collapse of the bubbles. The following modulations are only expected for oscillatory bubble motion.

An analysis of the equation of motion for a single transient bubble under a constant driving sound pressure can be performed by solving the Kirkwood-Bethe-Gilmore model. The best combination of sound pressure and initial bubble radius can be found by demanding a maximum bubble radius prior to collapse, a very small final radius and a collapse that is timed to be finished at the maximum positive pressure. 

Rayleigh 80) as early as 1917, developed an equation of motion for the collapse of a transient spherical cavity, assuming that both the pressure at infinity/ > and the pressure within the cavity were constant. Equating the kinetic energy of the... 

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