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Evolution of Staircase Structures in Diffusive Convection
Published on: September 5, 2018
Front waves and complex spatiotemporal patterns in a reaction-diffusion-convection system with thermokinetic
Tereza Trávnícková1, Martin Kohout, Igor Schreiber
1Department of Chemical Engineering and Center for Nonlinear Dynamics of Chemical and Biological Systems, Institute of Chemical Technology, Prague, Technicka 5, 166 28 Prague 6, Czech Republic.
Abstract:
We analyze dynamics of stationary nonuniform patterns, traveling waves, and spatiotemporal chaos in a simple model of a tubular cross-flow reactor. The reactant is supplied continuously via convective flow and/or by diffusion through permeable walls of the reactor. First order exothermic reaction kinetics is assumed and the system is described by mass and energy balances forming coupled reaction-diffusion-convection equations. Dynamical regimes of the reaction-diffusion subsystem range from pulses and fronts to periodic waves and complex chaotic behavior. Two distinct types of chaotic patterns are identified and characterized by Lyapunov dimension. Next we examine the effects of convection on various types of the reaction-diffusion regimes. Remarkable zigzag fronts and steady state patterns are found despite the absence of differential flow. We employ continuation techniques to elucidate the existence and form of these patterns.
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The collision theory is based on the postulates that (i) the reaction rate is proportional to the rate of reactant collisions, (ii) the reacting species collide in an orientation allowing contact between...

