Complex spatiotemporal patterns in an open-flow reactor

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Abstract
Reaction-diffusion systems in open-flow heterogeneous reactors are known to yield different instabilities and exhibit complex spatiotemporal dynamics. A particular mechanism leading to such behaviors is suggested here. Differential convection and differential diffusion can simultaneously induce instabilities at separate bands of wave numbers in an extended system where an activator-inhibitor reaction is taking place. The nonlinear interaction of these modes is shown to generate complex patterns with two different characteristic wavelengths and irregular temporal behavior in a distributed reactor for conditions at which a well-mixed reactor would exhibit no instability. The regions in the parameter space for two model kinetics where such patterns should exist are predicted a priori by normal form analysis of the relevant amplitude equations and validated with numerical simulations of the full partial differential equations. This mechanism for complex spatiotemporal behavior in open-flow reactors is expected to exist for many chemical reactions, including nonisothermal ones.