Motion bubble collapse time

It has been argued (Appendix 3, Eq. A.21) that the collapse time for a bubble, initially of radius R, is considerably shorter than the time period of the compression cyde. Thus the external pressure Pj (= P + Pjj), in the presence of an acoustic field, maybe assumed to remain effectively constant (Pj ) during the collapse period. Neglecting surface tension, assuming adiabatic compression (i. e. very short compression time), and replacing R, by R, the size of the bubble at the start of collapse, the motion of the bubble wall becomes... 

In Fig. 1.4a, an example of the radius-time curve for a stably pulsating bubble calculated by the modified Keller equation is shown for one acoustic cycle [43]. After the bubble expansion during the rarefaction phase of ultrasound, a bubble strongly collapses, which is the inertial or Rayleigh collapse. After the collapse, there is a bouncing radial motion of a bubble. In Fig. 1.4b, the calculated flux of OH... 

Figure 37-30, p. 443, shows an ultrasonic bath sieve cleaner. When ultrasonic energy waves are transmitted to a liquid, a pattern of microscopic bubbles forms and collapses immediately after generation. This rapid cavitation keeps particles in constant motion and frees lodged particles. It is most effective for fine mesh sizes up to about No. 30. Cleaning time is t ically 2 to 5 minutes. 

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. 

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