Bubble content effect Assume bubble contains non-condensable gas Partial pressure poo at reference size and temp. pa)=ma+o(是)（货） Te need to be determined,rewrite the R-P equation: pv(T)-Poe(t)pv(TB)-pv(To) PL PL （）() d2R 3 dR AvL dR 2S =R d2+2（ +R dt PLR First term is driving term Thermal term,which is considered later
Bubble content effect • Assume bubble contains non-condensable gas – Partial pressure at reference size and temp. • TB need to be determined, rewrite the R-P equation: – First term is driving term – Thermal term, which is considered later
Bubble content Taylor expansion on the first term Pv(TB)-PV(Too)=A(TB-Too) PL -A can be derived from Clausius-Clapeyron relation A=1= Pv(To)L(Too) PL dT PLToo 。Determine(Ts-To) -First step:heat diffusion equation,relates (Ta-T(ar/an +()买-是(） Second step:energy balance,relates (aT/ar),-R R(t). dR kL dt PyC r-R (TB-Too) R(t)
Bubble content • Taylor expansion on the first term – A can be derived from Clausius-Clapeyron relation • Determine – First step: heat diffusion equation, relates – Second step: energy balance, relates