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

Published online by Cambridge University Press:  20 April 2006

A. Biesheuvel  and
L. Van Wijngaarden
A. Biesheuvel
Affiliation:
Technological University Twente, Enschede, The Netherlands
L. Van Wijngaarden
Affiliation:
Technological University Twente, Enschede, The Netherlands
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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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 148 , November 1984 , pp. 301 - 318
Copyright
© 1984 Cambridge University Press

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