J. Krishnan
Department of Chemical Engineering
Princeton University

Patterns and their dynamics in catalytic CO oxidation

The catalytic oxidation of carbon monoxide on Pt(110) single crystal surfaces reveals a wide variety of spatiotemporal patterns. The length scale of these patterns is of the order of microns and they have been observed experimentally using Photo Emission Electron Microscopy. These patterns arise from the interplay of non-linear reaction and diffusional transport of the adsorbed species, and are modeled by reaction-diffusion equations of the activator-inhibitor type.

In this talk, we will focus on specific non-linear patterns and their dynamics. In these cases, the solution is not known in closed form, and therefore numerical methods are necessary. The PDE is discretized in space to yield a large dimensional dynamical system. Bifurcation analysis and numerical simulation are used to study this system.

The first problem to be considered is the dynamics of solitary pulses travelling with constant speed in 1-D. These are analyzed as steady states of the PDE in the co-moving frame. These undergo a variety of instabilities ranging from oscillatory instabilities to ``backfiring''. Then, motivated by experiments, we shall discuss rotating pulse-like structures in thin annular domains. In this case the pulse shape and speed vary depending on the location of the pulse in the annulus. This is because the diffusion of the adsorbed species on the underlying surface is anistropic. In the thin annulus limit, the problem can be reduced to a 1-D problem in a heterogeneous medium. We study the dynamics and instabilities of these rotating pulses. Since their shape and speed vary, numerical Floquet analysis is employed to determine their stability. Finally, we study the instabilities of a 1-D version of a target pattern in this system. Some of the instabilities seen here are also observed in other distributed chemical systems.