2 

 4ttR k (T -T) 

 . ^ c^ (25) 



k , here, being the conductivity, and 6 a heat diffusion distance. This 

 heat flux balances the evaporation requirement 



(* 



e 1^- ( 4 TTR 3 p„ ] 



and Plesset assumes 6 = /at, a being the thermal diffusivity. Bringing 

 these together we have 



p„< t >-J\,< t J . /e„\ 2 r 2 



ffte 



The other pressure differences are expressed in terms of the conventional 



cavitation number and pressure coefficient. To express the scale of the 



* * 



problem let t = t L/U , where t is a dimensionless time, and L and U are 

 c o o 



a reference length and speed, respectively. We may then write the right 



hand side of Equation (12) (neglecting, now, the viscous term) as 



U 2 , /2a __ \ /p \ 2 r 2 n . 



BB ..^ (0 + Cp(t)) .i(_..^.^) $.&.*& (27) 



IVo interesting, limiting cases are immediately evident: first, 



neglecting the thermal effect entirely, we estimate the asymptotic growth 



rate for an imposed constant value of (a + c ) . Then for R >> R we have 

 r p o 



the limiting "inertial" growth rate 



R. = U |- i (C7-+ c ) J 



l ° \ 3 P / 



(28) 



64 



