UBC Theses and Dissertations
Conservation laws in recombination kinetic theory Sze, Pui King Ivy
The hydrodynamic equations of change for a reacting gas mixture of monomers and dimers are studied. The gas is considered to be dilute and described by the kinetic theory of Lowry and Snider (J. Chem. Phys. 61, 2320 (1974)). From the kinetic equations for the density operators representing the monomer and dimer, the equations of change for one-molecule observables are obtained. Since the energy operator involves the intermolecular potential energy, it is necessary to derive the energy balance equation from the von Neumann equation, since this includes molecule-molecule correlations. As well, the kinetic theory formulated by Lowry and Snider is rewritten so that rearrangement collisions are emphasized. A collisional sum rule is derived involving the commutation properties of channel projectors and their respective potentials. A known property of the optical theorem is that it identifies the reactive loss terms as part of the non-reactive transition superoperators. The sum rule is applied to rewrite the non-reactive transition superoperators so as to display the reactive loss terms. This aids in establishing conservation laws for the physical observables of mass, linear momentum, angular momentum and energy. A form of the optical theorem in which kinetic energy off-diagonality is allowed for is also derived. Both the optical theorem and the sum rule are based on the strong orthogonality hypothesis, which plays a fundamental role in the Lowry-Snider theory. On localising the physical attributes at the centres of mass of the molecules, the contributions to the equations of change from collisional transfer (due to the forces and torques between the collision partners) and from the transfer of the physical attributes from the reactants to the products are identified. The transformation of dimer internal degrees of freedom into monomer translational degrees of freedom or vice versa when a dimer Is dissociated or formed is found to contribute to the equations of change by virtue of the differing locality of the collision partners. The decomposition of the kinetic energy operator into its components for radial and rotational motions allows the kinetic energy flux contributions associated with the pressure tensor and the molecular angular momentum flux to be identified.
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