Twophase flow equations for a dilute dispersion of gas bubbles in liquid
Biesheuvel, A. and Wijngaarden, L. van (1984) Twophase flow equations for a dilute dispersion of gas bubbles in liquid. Journal of fluid mechanics, 148 . pp. 301318. ISSN 00221120

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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 nonisotropic although the local stress tensors in the constituent phases are isotropic (viscosity is neglected). Next, by applying the same technique, the momentumflux 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 massconservation 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. 
Item Type:  Article 
Copyright:  © 1984 Cambridge University Press 
Faculty:  Science and Technology (TNW) 
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Link to this item:  http://purl.utwente.nl/publications/50418 
Official URL:  http://dx.doi.org/10.1017/S0022112084002366 
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