13 



Although a completely satisfactory theory of the liquid state still 

 remains to be formulated, it seems worth while to mention some of the results 

 of recent attempts to develop a kinetic theory of liquids. Recent work in the 

 "theory of nucleation" in condensed systems has led to clearer concepts of the 

 processes accompanying the formation of cavities in liquid, and leads to more 

 realistic estimates of the tensile strength of liquids. Although the methods 

 of nucleation theory apply both to the problems of cavity formation as well 

 as condensation, i.e., to phase transformations in general, these two aspects 

 of the cavitation process are here discussed separately. It is the view of 

 recent kinetic theories of the liquid state that the formation of vapor nuclei 

 proceeds from thermal or density fluctuations* in the interior of a liquid, 

 and that cavity growth takes place one molecule at a time as a result of these 

 statistical thermal fluctuations. If these holes or cavities reach a critical 

 size, they will continue to grow. The statistical conditions for such growth 

 have been investigated by Turnbull, Fisher, and Holloman 25 » 26 > 27 among 

 others, specifically for condensed systems, although similar methods have been 

 used to a much greater extent in the problem of condensation of supersaturated 

 vapors. The latter work is mentioned later. A more recent formulation of a 

 theory of condensed systems is given in Reference 28. The results given here 

 on cavity formation are taken primarily from the work of References 23, 25, 26, 

 and 27. 



To establish the critical size of cavity required for growth, we 

 compute the work associated with the reversible formation of a vapor bubble. 

 The work of formation of a cavity of volume V is pV. The work required for 

 the formation of the liquid -vapor interface of area A bounding the bubbles is 

 yA where y is the liquid-vapor surface tension. Finally, the work required to 

 fill the bubble reversibly with vapor at pressure p is - p V. Thus, the net- 

 work of formation of a spherical bubble of radius r is 



W = ^7rr 2 y + -=r7rr 3 (p - p ) 



For high negative pressures, the vapor pressure p may be neglected in com- 

 parison with p, so that the expression for the work simplifies to W = 4xrr 2 y + 



. 1677/ 



4 1 



7»rr p. The work is a maximum at 



W 

 max 



3p< 



*To be precise, one should speak of "energy fluctuations." However, for the present purpose, the 

 above terminology is believed to give a clearer physical picture. 



