Two-phase flow equations for a dilute dispersion of gas bubbles in liquid

A. Biesheuvel, L. van Wijngaarden

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Abstract

Equations of motion correct to the first order of the gas concentration by volume are derived for a dispersion of gas bubbles in liquid through systematic averaging of the equations on the microlevel. First, by ensemble averaging, an expression for the average stress tensor is obtained, which is non-isotropic although the local stress tensors in the constituent phases are isotropic (viscosity is neglected). Next, by applying the same technique, the momentum-flux tensor of the entire mixture is obtained. An equation expressing the fact that the average force on a massless bubble is zero leads to a third relation. Complemented with mass-conservation equations for liquid and gas, these equations appear to constitute a completely hyperbolic system, unlike the systems with complex characteristics found previously. The characteristic speeds are calculated and shown to be related to the propagation speeds of acoustic waves and concentration waves.
Original languageEnglish
Pages (from-to)301-318
JournalJournal of fluid mechanics
Volume148
DOIs
Publication statusPublished - 1984

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flow equations
two phase flow
Bubbles (in fluids)
Two phase flow
Tensors
bubbles
stress tensors
Liquids
liquids
Gases
gases
hyperbolic systems
conservation equations
Equations of motion
Conservation
Momentum
equations of motion
Acoustic waves
tensors
Viscosity

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Biesheuvel, A. ; van Wijngaarden, L. / Two-phase flow equations for a dilute dispersion of gas bubbles in liquid. In: Journal of fluid mechanics. 1984 ; Vol. 148. pp. 301-318.
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Two-phase flow equations for a dilute dispersion of gas bubbles in liquid. / Biesheuvel, A.; van Wijngaarden, L.

In: Journal of fluid mechanics, Vol. 148, 1984, p. 301-318.

Research output: Contribution to journalArticleAcademic

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AU - van Wijngaarden, L.

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