Kinetic theory of reacting fluid mixtures. I. The BBGKY hierarchy in arrangement channel quantum mechanics

Journal Article · Tue May 15 04:00:00 EDT 1979 · J. Chem. Phys.; (United States)

DOI:https://doi.org/10.1063/1.437299· OSTI ID:6330341

Hoffman, D K; Kouri, D J; Top, Z H

The statistical mechanics of reacting fluid mixtures is considered using arrangement channel quantum mechanics. In this theory, the many body wave function, psi, is expressed in terms of arrangement channel components psi/sub b/ which satisfy coupled time dependent equations. Using the properties of the psi/sub b/, we obtain the corresponding generalization of the density matrix rho denoted rho/sub alphabeta/ and the quantum ''Liouville equation'' which it satisfies. Reduced arrangement channel density matrices are introduced and are found to satisfy a generalization of the BBGKY hierarchy for reactive mixtures. The properties of the hierarchy are explored, and it is shown that the streaming terms in succeeding members of the hierarchy have increasing connectivity appropriate to the number of atoms in the contributing arrangement channels. The resulting hierarchy can serve as the rigorous starting point for developing statistical theories of reactive fluids. For example, it can be used to derive a Boltzmann equation appropriate to reacting gaseous mixtures.

• Research Organization: Ames Laboratory, USDOE and Department of Chemistry, Iowa State University, Ames, Iowa 50011
• OSTI ID: 6330341
• Journal Information: J. Chem. Phys.; (United States), Journal Name: J. Chem. Phys.; (United States) Vol. 70:10; ISSN JCPSA
• Country of Publication: United States
• Language: English

Related Subjects

640410* -- Fluid Physics-- General Fluid Dynamics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BBGKY EQUATION
BOLTZMANN EQUATION
DIFFERENTIAL EQUATIONS
DISPERSIONS
EQUATIONS
FLUIDS
FUNCTIONS
MECHANICS
MIXTURES
QUANTUM MECHANICS
STATISTICAL MECHANICS
WAVE FUNCTIONS