Experimental studies of the formation of Turing patterns in the (chlorine dioxide, iodine, malonic acid) reaction are performed in a spatial open gel disk reactor where all the input species are fed onto one side by a continuous stirred tank reactor. This setup is shown to fit the pool-chemical approximation used in most theoretical approaches. Nonequilibrium phase diagrams are established as a function of concentrations in the input flows. In agreement with theoretical predictions, the location of the transition from uniform steady states to Turing patterns is found to be almost independent of the concentrations of the complexing agent which controls the effective diffusion of activatory species. Extensive analytical and numerical calculations in two and three dimensions are performed on the basis of the Lengyel-Ra ´bai-Epstein kinetic model and its two-variable reduction. This particular experimental configuration is shown to minimize the problems encountered with more commonly used versions of spatial open reactors. In standard conditions, the quantitative agreement with the experiments is excellent in regard to the sketchiness of the model. Finally, we discuss the role of boundary conditions and comment on problems they raise in the use of one-side-fed open spatial reactors.
We show that the asymptotic method of Young and Boris is appropriate to the time integration of the stiff differential equations generated in the Fourier space when collocation spectral methods are applied to large reaction-diffusion model systems. This results in an easily implementable algorithm suitable for studies of morphology and stability of nonquilibrium structures in extended systems.
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