Some effects of spatial nonuniformities in chemically reacting mixtures

Citation

Coutsias, Evangelos A. (1980) Some effects of spatial nonuniformities in chemically reacting mixtures. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/3wt1-cc54. https://resolver.caltech.edu/CaltechTHESIS:12072012-130738166

Abstract

In Part I, a method is developed for treating reacting-diffusing systems whose kinetics lead to a limit cycle behavior with frequency varying slowly with position. This is accomplished by including the effects of the spatial variation in a phase variable that is introduced to parametrize the limit cycles at each point. The normalization of this phase variable is chosen such that the limit cycles at each point have the same frequency with respect to this variable. The method is motivated by treating the weakly coupled behavior of two oscillators that, unlike previous works, are not nearly identical. The analogy between discrete oscillator systems and continuous chemically reacting mixtures is explored by treating a chain of coupled limit cycle oscillators and considering various limits as the number of oscillators tends to infinity.

In Part II a different effect of spatial nonuniformities is studied: the modification of the simple diffusion approximation to treat situations of large deviations from equilibrium distributions in a mixture or proximity to some critical temperature. A technique for treating bifurcation from the continuous spectrum by introducing a slow space scale is developed. Using this, the onset of a spatially nonuniform state in a model chemically reacting system is studied, occurring when some reaction rate crosses the values at which linearized theory predicts destabilization of the uniform steady state solutions admitted by the system. Subs critical bifurcation is also found possible.

Thesis Files