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Characteristic stability parameter of the axisymmetric equilibrium surface of a capillary liquid

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Abstract

In [1] the question of stability of the equilibrium state of a capillary liquid in weak force fields was reduced to determination of conditions such that the smallest eigenvalue λ* of a certain boundary problem would be positive. In [2] it was shown that λ* is a monotonic function of the parameter χ, dependent on the form of the vessel. The basic properties of the function λ*(χ) were also described. In the present study, these properties are used to study the general problem of stability of an axisymmetric liquid surface. A method for calculation of the critical values of the parameter χ and construction of the maximum stability region is given. Special attention is given to the cases of complete weightlessness, and action of gravitational and centrifugal forces. Critical values of the parameter χ are presented for these cases either graphically or analytically, which, given the shape of the vessel, permits evaluation of the stability of any of the family of axisymmetric equilibrium surfaces. We note that in the case of action by gravitational forces χ values for certain equilibrium surfaces were obtained by Barnyak.

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Literature cited

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Authors
  1. L. A. Slobozhanin
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  2. A. D. Tyuptsov
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 74–84, July–August, 1974.

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Slobozhanin, L.A., Tyuptsov, A.D. Characteristic stability parameter of the axisymmetric equilibrium surface of a capillary liquid. Fluid Dyn 9, 563–571 (1974). https://doi.org/10.1007/BF01031314

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  • DOI: https://doi.org/10.1007/BF01031314

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