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Figure l6 - Time History of the Life of a Cavitation Bubble — Prom 

 Knapp and Hollander, Reference H-f 



DIFFUSION OF AIR INTO AN OSCILLATING CAVITY 



The diffusion of air into a cavity of the type considered here has 

 been studied analytically by Herzfeld and Pode and .some results are given by 

 Pode in a dissertation, Reference 49- Assuming that the dynamics of the mo- 

 tion of the cavity is not materially affected by the diffusion process, that 

 the gas cycle is adiabatic, that the gas density is uniform, and that the dif- 

 fusion process is confined to a thin surface layer, Pode shows that, for mo- 

 tions in which the maximum amplitude is double the equilibrium radius, the 

 order of the average rate of change of number of air molecules within the 

 cavity is 



dN 

 dt 



10' 



6^ 



Here, 6 is the thickness of the diffusion layer, 



R is the average radius of the cavity, 



N is the number of air molecules in the bubbles, and 



Nj_ is the initial number of air molecules. 



A further result is that the diffusion into the cavity increases with increas- 

 ing ratio of maximum amplitude to equilibrium radius. From the above result 

 it is seen that, on the average, the cavity continues to gain air molecules, 



