Boltzmann's equation for binary chemical reactions has been solved by the modified moment method using the equivalent of the 13-moment approximations. It was found that the transport coefficients are nonlinear in the thermodynamic forces. This nonlinearity is at least quadratic. The rate coefficient also appears to be at least quadratic in fluxes. / The stability of the solutions of two coupled equations of change for the current under the influence of an electric field is examined. These equations are deduced from the structure of dissipative terms calculated in the modified moment method. Two steady state branches in current are found to bifurcate from the primary steady state branch as a critical field value E(,c) = 4.35 V/cm is crossed. The results are in good qualitative agreement with experiment. / The dynamical behaviour of the two coupled equations used above was also studied in order to establish the influence (if any) of the entropy production surface on the trajectory followed by the system. This aspect of the study proved to be difficult since the entropy production surface associated with the two equations used did not have sufficiently distinctive features. / In order to continue studies on the relationship between dynamical behaviour and the topography of the entropy production surface, the two basic equations used before were slightly modified, and new parameters were introduced. At the critical field value E(,c) = 1.48 V/cm, no secondary steady states bifurcated out of the unstable primary steady state as in the previous model. Rather, stable oscillations in current of more or less constant amplitude occurred. This may account for some of the current fluctuations observed in experiment. The entropy production surface associated with this pair of model equations consists of two intersecting locii of minima. It turns out that the trajectory follows these minimal regions for most of the orbit, crossing from one locus of minima to another either through the intersection near to the origin or by crossing a ridge of high entropy production. The average energy dissipated over this cycle turns out to be smaller than if the system had remained with the unstable steady state. / Out of the latter studies, the useful conjecture was made. Given the topography of the entropy production surface and the stability of the steady states, it is possible to qualitatively predict the dynamics of the system provided the entropy production surface has sufficiently distinctive features.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.72014 |
| Date | January 1984 |
| Creators | Ali, Jaleel A. |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Doctor of Philosophy (Department of Chemistry.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 000222095, proquestno: AAINL20878, Theses scanned by UMI/ProQuest. |
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