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Atomization and Sprays

Journal of the International Institutes for Liquid Atomization and Spray Systems

ISSN for PRINT: 1045-5110

Institutional price:	$787.00
Issues per year:	8

Best Paper Award Selection - Editorial Board Site

2000, Volume10

318 pages

Issue price - $225.00

TOWARD A COMPREHENSIVE THEORY OF DENSE SPRAY FLOWS

Chris F. Edwards
Thermosciences Division, Department of Mechanical Engineering, Stanford University, Stanford, CA, USA

ABSTRACT

A mathematical theory of dense spray flows is described. It is based on treating the flow both inside and outside the drops via the incompressible Navier-Stokes equations and the interface as Gibbs' dividing surface. Taking into account the information necessary to describe the dynamical state of the flow, a hyperspace is constructed which describes the state of the system at any instant. This hyperspace consists of a number of field axes—one which describes the instantaneous velocity field and a number which describe the instantaneous morphology of the fluids.
Following the methods of statistical mechanics, an ensemble of macroscopically identical flows is used to define a density of system points in the hyperspace. A transport equation is then written which describes the evolution of this collection of flows for all time. A unique feature of this transport equation is that the dynamics of each fluid element are embedded in the transport equation—that is, the Navier-Stokes equations and interface jump conditions are implicit constraints on the overall transport of a system point in hyperspace.
The utility of the resulting equation (the continuum-particle, continuum-field equation) is demonstrated by showing that it can be reduced, in the limit of small dispersed-phase elements, to the point-particle, continuum-field equation which, in turn, has been shown to reduce to the ensemble-averaged Navier-Stokes and spray equations. As such, the present development is the uppermost level of a hierarchy of models for continuum treatment of spray flows—analogous to the Liouville equation of the kinetic theory of gases.