a constant. Second, we may now imagine that the thermal effect is large, 

 so that the bubble growth is slow. Then, the inertial terms on the left 

 hand side of Equation (12) may be imagined to be small. Again, for R >> R 

 bubble growth is then in thermal equilibrium with a rate 



R th " " -T (a + V * (29) 



\P / T 



k 



These rates can be quite different. In the first case we say that we 

 have "cavitation," and in the second, "boiling" is said to occur. The 

 ratio of the two rates may be expressed as 



!±_ 2 / t* / %) 2 J_ &L 

 R th "^ V " (a + V ^ P ' V- V " # 



(30) 



and for boiling to occur, the thermally controlled rate must be much less 

 than the inertial one, i.e., 



R. 



-±- » 1 (31) 



th 



This has led Brennen (1973) to identify the dimensional group of terms 



Z<¥) 



2 jL. i 



c T j- 

 p °° /a 



(32) 



as the "thermal parameter" of importance and thence, if 



65 



