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Liquid bridges and black strings in higher dimensions · Around

2008

Liquid bridges and black strings in higher dimensions

Miyamoto, Umpei, Maeda, Kei-ichi

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Analyzing a capillary minimizing problem for a higher-dimensional extended fluid, we find that there exist startling similarities between the black hole-black string system (the Gregory-Laflamme instability) and the liquid drop-liquid bridge system (the Rayleigh-Plateau instability), which were first suggested by a perturbative approach.

In the extended fluid system, we confirm the existence of the critical dimension above which the non-uniform bridge (NUB, i.e., {\it Delaunay unduloid}) serves as the global minimizer of surface area.
We also find a variety of phase structures (one or two cusps in the volume-area phase diagram) near the critical dimension.
Applying a catastrophe theory, we predict that in the 9 dimensional (9D) space and below, we have the first order transition from a uniform bridge (UB) to a spherical drop (SD), while in the 10D space and above, we expect the transition such that UB $\to$ NUB $\to$ SD.

Built on

W.W. Mullins, J. Appl. Phys. 28
1957
Earlier work this paper cites.
F.A. Nichols and W.W. Mullins, J. Appl. Phys. 36
1965
Earlier work this paper cites.
J.D. Bekenstein, Phys. Rev. D 7
1973
Earlier work this paper cites.
K.S. Thorne, D.A. MacDonald, and R.H. Price, Black Holes: The Membrane Paradigm
1986
Earlier work this paper cites.
R. Finn, Equilibrium Capillary Surfaces
1986
Earlier work this paper cites.
T.I. Vogel, SIAM J. Appl. Math. 47
1987
Earlier work this paper cites.
J. Eggers, Phys. Rev. Lett. 71
1993
Earlier work this paper cites.
R. Gregory and R. Laflamme, Phys. Rev. Lett. 70
1994
Earlier work this paper cites.

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