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The Rayleigh-Plesset Equation for Sonoluminescence

  1. Oct 10, 2012 #1
    I'm investigating the phenomenon of sonoluminescence. A quick search has yielded the Rayleigh-Plesset equation as being of use.
    [tex]\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}[/tex]

    A brief look on the wikipedia entry on sonoluminescence yields an approximate form.
    [tex]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)[/tex]

    Now I'm assuming that P0 = PB and P = Pinfinite. So that gives (when rearranged):

    [tex]\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} [/tex]

    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.
  2. jcsd
  3. Oct 11, 2012 #2


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  4. Oct 13, 2012 #3
    Thank you.

    I've managed to get a very faint green streak on a long exposure. It's quite a lovely effect.
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