Analytical approximations for the collapse of an empty spherical bubble.

@article{Obreschkow2012AnalyticalAF,
  title={Analytical approximations for the collapse of an empty spherical bubble.},
  author={Danail Obreschkow and Martin Bruderer and Mohamed Farhat},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2012},
  volume={85 6 Pt 2},
  pages={066303}
}
The Rayleigh equation 3/2R+RR+pρ(-1)=0 with initial conditions R(0)=R(0), R(0)=0 models the collapse of an empty spherical bubble of radius R(T) in an ideal, infinite liquid with far-field pressure p and density ρ. The solution for r≡R/R(0) as a function of time t≡T/T(c), where R(T(c))≡0, is independent of R(0), p, and ρ. While no closed-form expression for r(t) is known, we find that r(0)(t)=(1-t(2))(2/5) approximates r(t) with an error below 1%. A systematic development in orders of t(2… CONTINUE READING

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