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Stability of gas-bubble equilibrium shape in uniform flow of an ideal fluid

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Abstract

Steady-state motion of a bubble in the shape of an ellipsoid of revolution has been studied [1, 2]. Steady-state motion and small oscillations of an ellipsoid of revolution around the equilibrium state were studied with the help of Lagrangian equations [3]. In this paper, possible equilibrium shapes of a bubble in the form of a triaxial ellipsoid are studied. The dependence of the pressure difference at the stagnation point and within the gas bubble on deformation is determined for steady-state motion. The stability of the equilibrium shape with respect to small perturbations of the axes of the ellipsoid is investigated through analysis of potential energy in the neighborhood of the extremum.

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Literature cited

  1. O. M. Kiselev, “Determination of gas-bubble shape in axisymmetric flow of fluid,” Zh. Prikl. Mekhan. Tekh. Fiz., No. 3 (1963).

  2. D. W. Moore, “The velocity of rise of distorted gas bubbles in a liquid of small viscosity,” J. Fluid Mech.,23, No. 4 (1965).

  3. O. V. Voinov, A. M. Golovin, and A. G. Petrov, “Motion of ellipsoidal bubble in fluid of low viscosity,” Zh. Prikl. Mekhan. Tekh. Fiz., No. 3 (1973).

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  6. O. M. Kiselev, “Problem of a gas bubble in plane flow of an ideal fluid,” Izv. Akad. Nauk SSSR, Mekhan. Zhidk. i Gaza, No. 4 (1969).

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Authors and Affiliations

  1. Moscow

    A. G. Petrov

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  1. A. G. Petrov
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Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 49–54, September–October, 1974.

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Petrov, A.G. Stability of gas-bubble equilibrium shape in uniform flow of an ideal fluid. J Appl Mech Tech Phys 15, 623–627 (1974). https://doi.org/10.1007/BF00851519

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  • DOI: https://doi.org/10.1007/BF00851519

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