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Multiphase Science and Technology

ISSN Print: 0276-1459
ISSN Online: 1943-6181

Multiphase Science and Technology

DOI: 10.1615/MultScienTechn.v18.i2.20
pages 135-154

SYSTEMATIC APPROACH TO CLOSURE RELATIONS FOR DISPERSE PARTICLE FLOWS: INTER-PHASE FORCE

A. Prosperetti
Department of Mechanical Engineering, The John Hopkins University, Baltimore, MD 21218, USA; and Department of Applied Physics, IMPACT, University of Twente, AE 7500 Enschede, The Netherlands
K. Ichiki
Department of Chemistry, University of Western Ontario, Ontario N6A 5B7, Canada
Q. Zhang
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore MD 21218, USA

ABSTRACT

The closure of the equations obtained by formal averaging of the microscopic laws of motion for particles in a fluid remains an important open problem in the theory of disperse flows. This paper gives a form for the particle and fluid momentum equations expressed in terms of computable quantities and derives a closure relation for the inter-phase force. It is shown that, in the derivation, it is essential to address the spatially non-uniform situation to find a valid relation and a method to carry out ensemble averaging for this situation is described.