XII 

 PHYSICAL EFFECTS IN CAVITATION AND BOILING 



M. S. Plesset 

 California Institute of Technology 



Introduction 



The problem to be considered here is the growth of a vapor bubble in a super- 

 heated liquid. When the vapor pressure of the liquid exceeds the ambient pressure, 

 it becomes possible for a vapor bubble to grow from a small "nucleus" in the liquid. 

 This nucleus is a region of nonliquid phase and presumably consists of a gas or vapor 

 phase stabilized on a solid particle. The factors which affect the rate of bubble growth 

 are the surface tension, the liquid inertia, and the difference between the pressure within 

 the bubble and the ambient or external pressure. We shall suppose that the bubble 

 begins its growth near the condition of equilibrium of the forces acting upon it. The 

 initial growth will be slow, but it is accelerated with increase in size because of the 

 reduction in surface tension. When the rate of bubble growth becomes appreciable, 

 however, the temperature, and hence the pressure within the bubble, drops and the 

 rate of growth is decreased. One therefore might expect a maximum in the velocity of 

 the bubble wall. The reduction of the temperature within the bubble is a consequence 

 of the latent heat requirement of the evaporation which takes place at the vapor-liquid 

 interface as the bubble grows. 



Formulation of the Problem 



For a quantitative solution of the problem, some simplifying assumptions may 

 be made. These simplifications will be presented for the example of a vapor bubble 

 growing in moderately superheated water. It will be assumed that the bubble is 

 spherical throughout its growth. One can show that the spherical shape is stable for 

 a growing bubble in a spherically symmetric pressure field [1]. We are clearly exclud- 

 ing from consideration the asymmetric buoyant force of gravity which becomes 

 important if the bubble growth is followed for so long a time that a significant trans- 

 lational velocity is acquired. A translational velocity of the bubble as a whole not only 

 causes a deformation of shape but also increases the rate of heat inflow over that 

 used in the present analysis. In water superheated by about 10°C no great error is 

 introduced by the buoyant force provided the bubble growth is not followed beyond 

 a radius of 1 mm or for a time longer than a few milliseconds. 



With a superheat of the order of 10°C at one atmosphere pressure, a vapor 

 bubble grows from its initial microscopic size of approximately 10 -3 mm to a radius of 

 1 mm in a time of the order of 10 millisec. The corresponding average radial velocity 

 is 10 cm/sec. The maximum radial velocity is about 10 times this value. We see that 

 the velocities of concern in the bubble growth are very small compared with the sound 

 velocity in either the liquid or the vapor. The hydrodynamic equation of motion which 

 contains the effect of liquid inertia is thus rather simple: the liquid motion of concern 

 is incompressible and spherically symmetric. With the limitation to irrotational flow 

 one has the velocity potential 



RR 2 



<P = , (1) 



r 



297 



