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Introduction. General Principles of Description of Two-Phase Systems

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Bubble Systems

Part of the book series: Mathematical Engineering ((MATHENGIN))

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Abstract

The general concept of the two-phase systems and their classification is presented. Basic methods of two-phase flows description are discussed: method of detailed description, unit cell models, single continuum models, models of multispeed medium. The main problems and limitations of existing approaches to the development of mathematical models are shown. It turned out that the correct choice of the coordinate system in many cases can simplify the description of the two-phase systems. The examples describing the typical two-phase systems behaviour in ‘laboratory coordinate system’ and in ‘native coordinate system’ are presented. The detailed study of the problem of the proper assignment of the ‘coupling conditions’, which are 'inner' boundary conditions written on the boundaries of coexisting phases is carried out. The general equations governing the coupling conditions were derived, and then reduced for a broad set of individual cases of practical and scientific interest. The basic approach to the determination of the intensity of nonequilibrium phase transitions in two-phase flows is presented. Finally, the structure of the book is described and a brief content of the individual chapters is presented.

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Notes

  1. 1.

    Small in the scale of variation of quantities characterizing the motion of liquid.

  2. 2.

    It is assumed that the property P varies continuously within each of the one-phase volumes \(V_{l}\) and \(V_{v}\), discontinuities are possible only on the interfacial surface \(\varDelta S\).

  3. 3.

    It is assumed that the surface tension coefficient is constant along the interface surface.

  4. 4.

    Or, what is the same, by moving the interfacial boundary in the laboratory coordinate system related to the bulk of liquid at rest.

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Authors and Affiliations

  1. Dmitrovskoe shosse 46-1-6, 127238, Moscow, Russia

    Alexander A. Avdeev

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  1. Alexander A. Avdeev
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Correspondence to Alexander A. Avdeev .

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Avdeev, A.A. (2016). Introduction. General Principles of Description of Two-Phase Systems. In: Bubble Systems. Mathematical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-29288-5_1

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  • DOI: https://doi.org/10.1007/978-3-319-29288-5_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-29286-1

  • Online ISBN: 978-3-319-29288-5

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