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Variational principles and two-fluid hydrodynamics of bubbly liquid/gas mixtures

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  • Geurst, J.A.

Abstract

In a recent paper the two-phase flow equations for a bubbly liquid/gas mixture were derived by variational methods. Starting point was an Euler form of Hamilton's extended principle of least action. The effect of the virtual mass of the gas bubbles was included. It is demonstrated now that a variational principle in the Langrange form yields the same two-fluid equations. In addition it is shown how the Lagrange form is trandformed in the Euler form by means of a canonical transformation. With regard to a recent discussion in the literature the material frame indifference or objectivity of the virtual-mass terms is investigated. The mutual force between the two-phases which is associated with the virtual mass of the gas bubbles turns out to be objective. In the limit of low bubble concentrations the results of the one-bubble theory are recovered. A corrected value is derived for the lift coefficient of a gas bubble in a rotational flow. It is indicated how a scheme of iterative solutions yields higher order approximations in which the mutual interaction of the gas bubbles is taken into account.

Suggested Citation

  • Geurst, J.A., 1986. "Variational principles and two-fluid hydrodynamics of bubbly liquid/gas mixtures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 135(2), pages 455-486.
    • Handle: RePEc:eee:phsmap:v:135:y:1986:i:2:p:455-486
    DOI: 10.1016/0378-4371(86)90154-8
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