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On the quest for a hyperbolic effective-field model of disperse flows

Published online by Cambridge University Press:  14 August 2013

Daniel Lhuillier ,
Chih-Hao Chang  and
Theo G. Theofanous
Daniel Lhuillier
Affiliation:
Institut Jean le Rond d’Alembert, UPMC Université Paris 6 and CNRS (UMR 7190), F-75005 Paris, France
Chih-Hao Chang
Affiliation:
Chemical Engineering Department, University of California, Santa Barbara, CA 93106, USA
Theo G. Theofanous*
Affiliation:
Chemical Engineering Department, University of California, Santa Barbara, CA 93106, USA
*
†Email address for correspondence: daniel.lhuillier@upmc.fr
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Abstract

The cornerstone of multiphase flow applications in engineering practice is a scientific construct that translates the basic laws of fluid mechanics into a set of governing equations for effective interpenetrating continua, the effective-field (or two-fluid) model. Over more than half a century of development this model has taken many forms but all of them fail in a way that was known from the very beginning: mathematical ill-posedness. The aim of this paper is to refocus awareness of this problem from a unified fundamental perspective that clarifies the manner in which such failures took place and to suggest the means for a final closure.

JFM classification

Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows Multiphase and Particle-laden Flows: Multiphase flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 731 , 25 September 2013 , pp. 184 - 194
Copyright
©2013 Cambridge University Press 

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