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Bubbles in liquids with phase transition

Part 1. On phase change of a single vapor bubble in liquid water

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Abstract

In the forthcoming second part of this paper a system of balance laws for a multi-phase mixture with many dispersed bubbles in liquid is derived where phase transition is taken into account. The exchange terms for mass, momentum and energy explicitly depend on evolution laws for total mass, radius and temperature of single bubbles. Therefore in the current paper we consider a single bubble of vapor and inert gas surrounded by the corresponding liquid phase. The creation of bubbles, e.g. by nucleation is not taken into account. We study the behavior of this bubble due to condensation and evaporation at the interface. The aim is to find evolution laws for total mass, radius and temperature of the bubble, which should be as simple as possible but consider all relevant physical effects. Special attention is given to the effects of surface tension and heat production on the bubble dynamics as well as the propagation of acoustic elastic waves by including slight compressibility of the liquid phase. Separately we study the influence of the three phenomena heat conduction, elastic waves and phase transition on the evolution of the bubble. We find ordinary differential equations that describe the bubble dynamics. It turns out that the elastic waves in the liquid are of greatest importance to the dynamics of the bubble radius. The phase transition has a strong influence on the evolution of the temperature, in particular at the interface. Furthermore the phase transition leads to a drastic change of the water content in the bubble. It is shown that a rebounding bubble is only possible, if it contains in addition an inert gas. In Part 2 of the current paper the equations derived are sought in order to close the system of equations for multi-phase mixture balance laws for dispersed bubbles in liquids involving phase change.

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Authors and Affiliations

  1. Weierstrass Institute, Mohrenstr. 39, 10117, Berlin, Germany

    Wolfgang Dreyer

  2. Howaldswerke-Deutsche Werft GmbH, Werftstr. 112-114, Kiel, Germany

    Frank Duderstadt

  3. Institute for Analysis and Numerics, Otto-von-Guericke-University Magdeburg, PSF 4120, 39016, Magdeburg, Germany

    Maren Hantke & Gerald Warnecke

Authors
  1. Wolfgang Dreyer
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  2. Frank Duderstadt
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  3. Maren Hantke
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  4. Gerald Warnecke
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Corresponding author

Correspondence to Maren Hantke.

Additional information

Communicated by Oliver Kastner.

This work was supported by the DFG grant Wa 633/17 within the DFGCNRS research group FOR 563/1 and by the DFG grant DR 401/4-1. The authors thank the DFG for this funding.

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Dreyer, W., Duderstadt, F., Hantke, M. et al. Bubbles in liquids with phase transition. Continuum Mech. Thermodyn. 24, 461–483 (2012). https://doi.org/10.1007/s00161-011-0225-6

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  • DOI: https://doi.org/10.1007/s00161-011-0225-6

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