11 

 DYNAMICS OF TRANSIENT CAVITIES 

 THE MOTION OF SMALL TRANSIENT CAVITIES 



Since, in Reference 3, a brief outline of the experimental observations on transient 

 cavities up to 1950 was given, only a few remarks will be made here in connection with an 

 apparent difference in experience among different investigators on the rebound of such cavi- 

 ties. For this discussion, we exclude observations in which magnetostriction oscillators or 

 ultrasonic fields were used to cavitate the liquid. Also excluded are experiments in which 

 small air bubbles were introduced to assist the formation of the cavity. 



In 1928, Mueller^^ published prints of motion picture frames showing cavitation on a 

 hydrofoil. These photographs showed clearly the growth and collapse of individual cavities, 

 but no oscillations were observed. Harvey et al,^"* using rods withdrawn rapidly from a liquid, 

 obtained several oscillations of the resultant cavity and attributed them to energy storage in 

 air entrained in the bubble. Knapp and Hollander, ^^ in a now classical series of photographs, 

 showed several cycles in the oscillations of cavities in a flowing liquid. They argued that 

 in their experiments the initial air content of the cavities was extremely small and attributed 

 the rebound of the cavity primarily to the storage of energy in the liquid in elastic compres- 

 sion, with this stored energy subsequently producing the outward radial velocity. 



More recently, experiments by Harrison ^^ have shown that cavities formed in water of 

 low air content do not rebound, and the conclusion was reached that only cavities containing 

 a large amount of gas will oscillate. In a private communication, Dr. M.S. Plesset informed 

 the writer that the same results were recently obtained at the California Institute of Technol- 

 ogy. It may, therefore, be concluded that in liquid of low aircontent, the effects of compress- 

 ibility and viscosity in both the liquid and gas phases in dissipating energy are such as to 

 allow no rebound if there is only a small amount of permanent gas in the bubble. However, no 

 consideration appears to have been given as to what this lower limit of initial air content in 

 the nucleus must be to prevent rebounds. 



ANALYTICAL DESCRIPTION OF THE MOTION 



Work on the motions of a spherical cavity in an incompressible fluid in which the role 

 of the gas within the bubble is neglected was reviewed in Reference 3. These theories give 

 adequate descriptions of the motion for the largest part of the cycle of such bubbles but are 

 inadequate toward the end of the collapse stage where compressibility and viscosity effects 

 in both the liquid and the gas phase become of importance. This was shown by the computa- 

 tions of Plesset as compared with the experimental results of Knapp and Hollander. Dis- 

 crepancies noted between theory and observation for the collapse part of the cycle were attri- 

 buted to wall effects—the bubbles having been formed near a model and these effects neglect- 

 ed. This was clearly shown by Rattray '^'^ in a dissertation in which he computed the motion 

 of such cavities when near a plane wall. The analysis is too lengthy to give details here, 



