- #1
Ashiataka
- 21
- 1
I'm investigating the phenomenon of sonoluminescence. A quick search has yielded the Rayleigh-Plesset equation as being of use.
\frac{P_B(t)-P_\infty(t)}{\rho_L}=R\frac{d^2R}{dt^2}+\frac{3}{2}\left( \frac{dR}{dt}\right)^2+\frac{4\nu_L}{R}\frac{dR}{dt}+\frac{2S}{\rho_LR}
A brief look on the wikipedia entry on sonoluminescence yields an approximate form.
R\frac{d^2R}{dt^2} + \frac{3}{2}\left( \frac{dR}{dt}\right)^2 = \frac{1}{\rho}\left(p_g - P_0 - P(t) - \frac{4\nu_L}{R} \frac{dR}{dt} - \frac{2S}{R}\right)
Now I'm assuming that P0 = PB and P = Pinfinite. So that gives (when rearranged):
\frac{P_B(t) + P_\infty(t)}{\rho_L} + R\frac{d^2R}{dt^2} + \frac{3}{2}\left( \frac{dR}{dt}\right)^2 + \frac{2S}{\rho_LR} = \frac{p_g }{\rho_L}-\frac{4\nu_L}{\rho_LR} \frac{dR}{dt}
which has the two terms on the RHS being different from the original expression. Firstly, what is pg? And secondly, why do both terms now have a 1/rho factor?
Thank you.
\frac{P_B(t)-P_\infty(t)}{\rho_L}=R\frac{d^2R}{dt^2}+\frac{3}{2}\left( \frac{dR}{dt}\right)^2+\frac{4\nu_L}{R}\frac{dR}{dt}+\frac{2S}{\rho_LR}
A brief look on the wikipedia entry on sonoluminescence yields an approximate form.
R\frac{d^2R}{dt^2} + \frac{3}{2}\left( \frac{dR}{dt}\right)^2 = \frac{1}{\rho}\left(p_g - P_0 - P(t) - \frac{4\nu_L}{R} \frac{dR}{dt} - \frac{2S}{R}\right)
Now I'm assuming that P0 = PB and P = Pinfinite. So that gives (when rearranged):
\frac{P_B(t) + P_\infty(t)}{\rho_L} + R\frac{d^2R}{dt^2} + \frac{3}{2}\left( \frac{dR}{dt}\right)^2 + \frac{2S}{\rho_LR} = \frac{p_g }{\rho_L}-\frac{4\nu_L}{\rho_LR} \frac{dR}{dt}
which has the two terms on the RHS being different from the original expression. Firstly, what is pg? And secondly, why do both terms now have a 1/rho factor?
Thank you.