Analysis and modeling of pattern formation in catalytic systems

Heterogeneous catalytic reactions are known to exhibit a variety of spatiotemporal patterns. The formation of temperature and concentration patterns on a catalytic surface can significantly alter the yield of reaction as well as disguise the intrinsic kinetics, so that kinetic parameter values found in the laboratory will not be useful for scale-up. Despite its importance not only in catalysis, but in many other areas, the mechanism of pattern formation in heterogeneous systems is not well understood.;The isothermal and nonisothermal models with constant activity are shown to exhibit stationary temperature and concentration patterns for near stoichiometric composition of the reactants. The analysis shows that these stationary patterns exist in regions near the limit points and are likely to cause nonuniform ignition or extinction of the surface. It is found that the nonisothermal model with constant activity exhibits almost constant temperature moving concentration patterns near the homogeneous Hopf bifurcation point. The typical size of the patterns and the period of oscillation are estimated in terms of the various physico-chemical parameters.;The model with variable surface activity predicts only moving concentration and temperature patterns for typical parameter values. The analysis shows that these moving patterns are more likely to occur near the homogeneous Hopf bifurcation point indicating that spatially uniform oscillations are unlikely to be observed in practice. Some numerically simulated nonuniform stationary and moving patterns are presented.;In this work, we develop a hierarchy of models for pattern formation in heterogeneous catalytic systems. The models account for the diffusion of the species, conduction of heat in the catalyst, convection from the fluid phase to the surface, variation of the activity of the catalytic surface and Langmuir-Hinshelwood type kinetic mechanisms. Center Manifold and Bifurcation theory with O(2) symmetry, Singularity theory, and numerical spectral methods are used to determine the region of physico-chemical parameters in which stationary and moving patterns may exist.