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Influence of surface tension on the stability of heterogeneous equilibrium of barotropic liquid phases

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On the basis of the results of earlier work of the author [1] a study is made of the equilibrium and stability of a two-phase single-component heterogeneous liquid system with respect to perturbations of arbitrary shape. Allowance is made for the influence of surface tension, which plays a critical part in the formation of nucleating centers of a new phase [2]. Conditions of equilibrium are derived, and also a criterion of radial stability of a nucleating center of a new phase bounded by a closed spherical boundary. It is shown that radial stability of spherical nucleating centers also guarantees stability with respect to perturbations of arbitrary shape. The part played by the finite size of the system and the boundary conditions is elucidated. For this, two different cases are studied: a) a system under a constant external pressure, b) a system with fixed volume. In the first case, all equilibrium states are unstable. In the second, there are both unstable and stable configurations (depending on the corresponding values of two dimensionless parameters). The equation of the hyperbola of neutral stability is derived. The limits of a very small coefficient of surface tension and a very large size of the container are considered. The first situation corresponds to stable configurations, the second to unstable. For simplicity, the considered systems are assumed to be isothermal, and the equilibrium and stability are analyzed on the basis of the mechanical analog of Gibbs's principle, namely, the principle of a minimum of the mechanical potential energy of the barotropic heterogeneous liquid system. The case of nonisothermal perturbations leads to similar results, but the expressions for the corresponding dimensionless parameters are more cumbersome and less physically perspicuous.

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Literature cited

  1. 1.

    M. A. Grinfel'd, “Stability of heterogeneous equilibrium in a system with liquid phases,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 2, 88 (1982).

  2. 2.

    M. A. Leontovich, Introduction to Thermodynamics [in Russian], Gostekhizdat, Moscow-Leningrad (1952), p. 200.

  3. 3.

    V. F. Kagan, Fundamentals of the Tensor Theory of Surfaces, Part 1 [in Russian], Gostekhizdat, Moscow-Leningrad (1947), p. 512.

  4. 4.

    F. M. Morse and H. Feshbach, Methods of Theoretical Physics, Vols. 1 and 2, McGraw-Hill, New York (1953).

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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 3–8, May–June, 1983.

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Grinfel'd, M.A. Influence of surface tension on the stability of heterogeneous equilibrium of barotropic liquid phases. Fluid Dyn 18, 339–343 (1983).

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  • Surface Tension
  • Potential Energy
  • Dimensionless Parameter
  • Mechanical Analog
  • Finite Size