Bubble nucleation
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BUBBLEf o r m a t i o n is
a p h e n o m e n o n of wide t e c h n i cal i n t e r e s t . The n u c l e a t i o n of gas b u b b l e s i s i m p o r t ant, for e x a m p l e in the d e g a s s i f i c a t i o n of s t e e l and in the o p e r a t i o n of the h y d r o g e n bubble c h a m b e r ; e b u l l i t i o n , or b o i l i n g , is i m p o r t a n t in heat t r a n s f e r ; and the f r a c t u r e of liquids u n d e r h y d r o s t a t i c t e n s i o n p l a y s an i m p o r t a n t role in c a v i t a t i o n . In addition, b u b ble n u c l e a t i o n e x p e r i m e n t s provide one of the b e s t t e s t s of n u c l e a t i o n theory b e c a u s e of the r e l a t i v e l y s i m p l e g e o m e t r y of the c r i t i c a l n u c l e u s and of the r e l a tively few c o n t r i b u t i o n s to the free e n e r g y of f o r m a tion of the c r i t i c a l n u c l e u s . However, despite its i m p o r t a n c e , the n u c l e a t i o n theory for bubble f o r m a t i o n has not been t r e a t e d to the s a m e extent as the t h e o r i e s in o t h e r n u c l e a t i o n c a s e s . C l a s s i c a l theory and e x p e r i m e n t in bubble f o r m a t i o n have been r e v i e w e d r e c e n t l y , and the f o r m e r a m e n d e d s o m e w h a t , by H i r t h and Pound. 1 The t h e o r e t i c a l t r e a t m e n t s include those of D 6 r i n g , 2'3 B e r n a t h 4 Volmer,5 F i s h e r , 6 and W a k e s h i m a . 7 The F i s h e r - D S r i n g m o d e l , or its m o d i f i c a t i o n , 1 s a t i s f a c t o r i l y r a t i o n a l i z e s c a v i t a tion data. H o w e v e r , the t h e o r i e s have a n u m b e r of def i c i e n c i e s in the c a s e s of b o i l i n g or gas bubble f o r m a tion as d i s c u s s e d e x t e n s i v e l y by H i r t h and Pound. 1 The l a t t e r a u t h o r s have p r e s e n t e d , in o u t l i n e , a g e n e r a l t h e o r y for bubble n u c l e a t i o n . U n f o r t u n a t e l y , although the p r e e x p o n e n t i a l f a c t o r s a r e c o r r e c t l y p r e s e n t e d in t h e i r work and the final a n s w e r for the free e n e r g y of f o r m a t i o n of a c r i t i c a l - s i z e d bubble i s f o r t u i t o u s l y c o r r e c t , s e v e r a l e r r o r s a p p e a r e d in i n t e r m e d i a t e steps in d e r i v i n g the l a t t e r quantity. Landau and Lifshitz 6 cons i d e r only the f r e e e n e r g y of f o r m a t i o n d e s c r i b e d above and obtain the c o r r e c t final a n s w e r , but by the use of an i n c o n s i s t e n t t h e r m o d y n a m i c function. Hence, b e c a u s e of its i m p o r t a n c e and b e c a u s e we feel that none of the p r e v i o u s t r e a t m e n t s a r e e n t i r e l y c o r r e c t , we p r e s e n t an e x t e n d e d d e v e l o p m e n t of the theory h e r e , e m p h a s i z i n g the d e t e r m i n a t i o n of the free e n e r g y of f o r m a t i o n of the c r i t i c a l n u c l e u s . The f r e quency f a c t o r s for the n u c l e a t i o
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