Abstracts

Novosibirsk participants

Multiphase media are observed in various natural processes and widely used in various areas of human activity.

The dynamic stability and the stability of mixtures is very important for many technological operations, e.g., in space for noncontact crystallization of metals, growing of monocrystals, foamed metals, obtaining of various geometrical shapes, etc. [1].

The following fact is important for some technological processes (see [2]): a spherical bubble cannot be in equilibrium inside a liquid no matter how small the intensity of mass forces (it must only be nonzero). In this case a bubble, besides vibrations, begins to make forward motions.

The main principles of bubble hydrodynamics are formulated and the nonlinear equations of one-velocity bubble hydrodynamics are obtained in [3, 4]. The equations of motion are valid for an arbitrary density of bubbles and do not contain the description of the motion of an isolated bubble.

The problem of motion of bubbles in a liquid in a rigid vertical cylindrical container with a rigid base is considered in [5]. The container makes vertical vibrations with a displacement amplitude $Delta$ and an angular frequency $omega$ in the gravitational field. The equations of ideal liquid in a linear approximation serve as a basis for the model (see [5] and its references).

In this paper, a similar problem of the movement of bubbles in a vibrationg container is considered. The mathematical model describing the movement of bubbles in a liquid is based on a linear variant of bubble hydrodynamics taking into account the haracteristics of bubbles proposed in [4]. In this case the equations of motion of the carrier liquid are not the Cauchy-Kovalevskaya equations of time due to the presence of bubbles.

References

1. Ganiev R.F., Lapchinskii V.F. Problems of the Mechanics in Space Technology, Mashinostroyeniye, Moscow, (1978).
2. Moiseyev N.N., Rumyantsev V.V. The dynamics of a Body with Liquid-Containing Cavities, Nauka, Moscow, (1965).
3. Dorovsky V.N. A hydrodynamic nonlinear model of bubble liquid // Computers Math. Applic., v. 33, No 6, pp. 1-12, (1997).
4. Dorovsky V.N., Imomnazarov Kh.Kh., Romensky E.I. A hydrodynamic nonlinear model of bubble liquid (Part II) // Computers Math. Applic., v. 33, No. 6, pp. 13-15, (1997).
5. Nigmatulin R.I. The Dynamics of Multiphase Media. Part II, Nauka, Moscow, (1987).

Note. Abstracts are published in author's edition

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