by chemical reaction, which is in line with Mr. Gawn's remark, since according to 

 Griffing [4], free radicals are produced in the hot gas of a collapsing bubble. 



1. M. E. Fitzgerald, V. Griffing and J. Sullivan, T. Chem. Phys. 25 Oct. 1956; Wm. Batt, 



M. S. Thesis, Cath. Univ. 1956. 



2. F. E. Fox and K. F. Herzfeld, J. Acoust, Soc. Am. 26, 984 (1954). 



3. M. Strasberg, "The Onset of Ultrasonic Cavitation in Tap Water," Ph.D. Diss., Cath. 



Univ., 1956. 



4. V. Griffing, J. Chem. Phys. 18, 997, 1950; 20, 939, 1952. 



F. R. Gilmore 



The behavior of expanding vapor bubbles seems to be very well understood, 

 thanks to the good work of Professor Plesset and his students. I would like only to 

 make a few remarks on the related problem of collapsing vapor bubbles. Several 

 years ago I developed a theory which tries to take into account the compressibility of 

 the liquid, a factor which is important when the inward bubble wall velocity approaches 

 or exceeds the velocity of sound in the liquid [1]. This analysis is based on an 

 hypothesis due to Kirkwood and Bethe [2], the accuracy of which is very difficult 

 to assess. To check the validity of this analysis, I have integrated numerically the 

 partial differential equations for a bubble in water, collapsing under a constant pressure 

 difference of one atmosphere, using the "method of characteristics" and an IBM 604 

 computer. The results are shown in Fig. 1.* The calculated bubble-wall velocity 

 agrees within 6 per cent with that given by the analytic theory, over the calculated 

 range of 0.2 to 4.9 times the velocity of sound in water. The inward velocity thus 

 appears to increase like the radius to the minus one-half power as the radius becomes 

 small, instead of the minus first power given by acoustic theory, or the minus three- 

 halves power given by incompressible theory. 



1. F. R. Gilmore, "The Growth or Collapse of a Spherical Bubble, in a Viscous Compressible 



Liquid," Report No. 26-4, Hydrodynamics Laboratory, California Institute of Tech- 

 nology, April 1, 1952; published in part under the same title in Proceedings of the Heat 

 Transfer and Fluid Mechanics Institute Held at the University of California at Los 

 Angeles, June 24-26, 1952, p. 53. 



2. J. G. Kirkwood and H. A. Bethe, "The Pressure Wave Produced by an Underwater Explo- 



sion," OSRD Report No. 588, 1942. 



H. S. Preiser 



I would like to amplify the remarks of one of the previous speakers on the 

 possibility of cathodic protection relieving cavitation damage. 



Several experiments to this end were carried on in Italy during 1949 by 

 Professor G. Petracchi. Small metal specimens were suspended in the turbulent throat 

 of the venturi section of a water tunnel apparatus. Cavitation bubble collapse was 

 produced on the specimens. A method was incorporated into the experiment whereby 

 the specimens could be made the cathode of a simple electrolytic cell. Pit depth and 

 weight-loss measurements were taken on uncoupled specimens exposed to similar envi- 

 ronments. Those specimens under cathodic influence exhibited material resistance to 

 destruction when compared to similar specimens not under cathodic protection. 



There is ample opportunity to investigate the influence cathodic protection has on 

 cavitation damage by suitable experimental techniques. In fact, the Bureau of Ships 

 has set up such a program at the Boston Naval Shipyard. A model propeller has been 

 designed specially to produce excessive cavitation on the blades when rotating at 

 appropriate speeds. The cavitation pattern on the flat blades (bevelled edges) of the 

 propeller is controlled by variation of the pitch ratio and rotational speed. The pro- 



* Ed note: This figure appears on page 280, in Gilmore's discussion of the paper by 

 Fitzpatrick and Strasberg. 



320 



