Spatiotemporal patterns on cylindrical surfaces due to convection, conduction, and reaction

摘要

Spatiotemporal patterns emerging on a cylindrical surface, representing an annular reactor with convection in the axial direction, are simulated with a model that incorporates an activator and a slow changing and localized inhibitor. This condensed polynomial model captures the main features of high-or low-pressure catalytic oscillations. The results are organized in bifurcation diagrams showing the coexisting solutions with varying convection. Steady rotating band solutions, that emerge with proper initial conditions, exist for sufficiently low fluid velocity (V) and bifurcate to steady patterns for a bistable kinetics. For the oscillatory kinetics the rotating solutions coexist with the oscillatory solutions that are independent of the angular coordinate. For large V a single homogeneous solution exists, which is mainly defined by the inlet boundary condition. In the limit of a very long cylinder, helix-shape rotating band may exist, allowing one to gain some insight into analytical solutions.