In Eq. (7), a is the accommodation coefficient and y is the ratio of specific heats, a is 

 not known at the temperatures of present interest; it has been measured to be 0.04 for 

 water at 0°C. This would give c* — 8 m/sec. There is some basis for believing that a 

 is larger than 0.04 at the temperatures of concern here, but in any case the pressure of 

 the vapor is essentially the same as the equilibrium vapor pressure. 



We may consider finally the temperature within the bubble. In general the 

 temperature of the vapor would vary with position as well as with time. The thermal 

 diffusivity of the vapor, D', is significantly larger than the thermal diffusivity of the 

 liquid, and the characteristic diffusion length in the vapor, y/D't, is large compared with 

 the bubble radius. We may therefore make the approximation that the temperature is 

 uniform in the bubble. 



In summary, the physical model upon which the analysis is based consists of a 

 spherical vapor bubble which has uniform temperature and pressure, the temperature of 

 the vapor is that of the liquid at the bubble wall, and the pressure is the equilibrium 

 vapor pressure for that temperature. In addition, the effects of viscosity and compres- 

 sibility may be neglected. 



The Equation of Motion and the Boundary Conditions 



We have seen that the viscous effect is negligible in the energy equation and we 

 shall show that it is also negligible in our boundary condition. In the equation of motion 

 for the bubble (Eq. (3)), one needs the pressure p(R) in the liquid at the bubble wall; 

 this pressure is related to the pressure in the vapor p r by 



2<x R 



p{R) = p,.(T) 4 M - . (8) 



R R 



The effect of viscosity is to increase the surface tension by l^R, and this increase is 

 about 0.5 dyne/an and is therefore negligible. We shall therefore write 



2(7 



p(R) = p v (T) - - . (9) 



R 



The boundary condition for the heat equation 



ST 



P c v h v ■ VT = kAT + q (10) 



dt 



may be simply deduced in the following way. The heat Q which must be supplied to 

 the bubble per unit time is 



4-7T d 



Q = —L-(R*p') (11) 



3 dt 



where L is the latent heat of evaporation per unit mass and p' is the vapor density. This 

 heat is supplied by conduction into the bubble so that 



( dT \ 



Q = -inR^k — (12) 



\ dr / r =R 

 where k is the thermal conductivity of the liquid. Hence 



dT\ Lid 



— = (flV). (13) 



dr ) R 3kR 2 dt 



299 



