We analyze the Rayleigh equation for the collapse of an empty bubble and provide an explanation for some recent analytical approximations to the model. We derive the form of the singularity at the second boundary point and discuss the convergence of the approximants. We also give a rigorous proof of the asymptotic behavior of the coefficients of the power series that are the basis for the approximate expressions.
REFERENCES
1.
D.
Obreschkow
, P.
Kobel
, N.
Dorsaz
, A. de
Bosset
, C.
Nicollier
, and M.
Farhat
, Phys. Rev. Lett.
97
, 094502
(2006
).2.
D.
Obreschkow
, M.
Tinguely
, N.
Dorsaz
, P.
Kobel
, A. de
Bosset
, and M.
Farhat
, Phys. Rev. Lett.
107
, 204501
(2011
).3.
D.
Obreschkow
, M.
Bruderer
, and M.
Farhat
, Phys. Rev. E
85
, 066303
(2012
).4.
Lord
Rayleigh
, Philos. Mag.
34
, 94
(1917
).5.
M. S.
Plesset
, Ann. Rev. Fluid. Mech.
9
, 145
(1977
).6.
A.
Prosperetti
, Phys. Fluids
30
, 3626
(1987
).7.
P.
Amore
and F. M.
Fernández
, J. Phys. A
41
, 025201
(2008
).8.
P.
Amore
, Phys. Rev. D
76
, 076001
(2007
).© 2013 American Institute of Physics.
2013
American Institute of Physics
You do not currently have access to this content.
