TABLE 2 - SOME VALUES OF NATURAL FREQUENCY AND 

 CRITICAL RADIUS FOR BUBBLES 



R 

 o 



a 







(p -p =0.1 atm) 



00 V 



^--Vcrit 



10 -6 m 



2 x 10 6 Hz 



1.21 atm 



10~ 5 m 



1 x 10 5 Hz 



0.12 atm 



10~ 4 m 



1 x 10 4 Hz 



0.01 atm 



Before continuing on to consider how these results might be used in 

 interpreting cavitation inception, we pause briefly to consider the vapor 

 pressure term, p , and how it may be expected to change during bubble 

 growth. The basic idea is that bubble growth implies evaporation of liquid 

 and, hence, cooling of the bubble wall. This cooling depresses the vapor 

 pressure and, hence, tends to reduce the pressure difference available for 

 growth. Rough ideas of the magnitude of the "thermal effect" are easily 

 obtained following physical arguments due to Plesset (1949) . The pressure 

 difference terms, on the right hand side of Equation (12), are split up as 

 follows (see also Holl and Kornhauser 1970) 



p (T)-p (t) = p (T )-p (t=0) + p (t=0)-p (t) + p (T)-p (T ) (23) 



r Y r oo v ' V °° oo ' r oo^ ' r oo v ' v V °° 



where (°°) means far from the body, and T is the temperature of the liquid 

 at the bubble wall. The vapor pressure difference is estimated from the 

 Clausius-Clapeyron equation to be 



P V (T) - P V (.TJ = ^- P V (T-TJ 



(24) 



where p is the density of the vapor and £ is the latent heat. The heat 

 flow supporting the evaporation is (approximately) 



63 



