Analysis of concentration and temperature patterns on catalytic surfaces

Abstract

A simple mathematical model for pattern formation on isothermal as well as nonisothermal catalytic surfaces is developed and analyzed. The model accounts for diffusion of the species, conduction of heat, convection from the fluid phase, and a bimolecular Langmuir–Hinshelwood type kinetic expression. The isothermal model is shown to exhibit stationary concentration patterns for typical sets of parameters. The nonisothermal model exhibits stationary temperature and concentration patterns only for near stoichiometric composition of the reactants (three equation model). The calculations show that these stationary patterns exist in regions near the ignition and extinction points and are most likely to form during ignition or extinction of the surface. It is also found that moving concentration and temperature patterns exist near the Hopf bifurcation point of the ignited homogeneous branch. The moving patterns predicted for realistic values of the transport and kinetic parameters are concentration patterns with almost constant temperature distribution on the surface. The typical size of the patterns and the period of oscillation are estimated in terms of the physicochemical parameters.