Regular and Chaotic Chemical Spatiotemporal Patterns

Abstract

The first experimental observation of a bifurcation sequence of patterns in a reaction-diffusion system is reported. The experiment on a one-dimensional system, maintained away from equilibrium, reveals steady, periodic, quasiperiodic, frequency-locked, period-doubled, and chaotic spatiotemporal states. Results from a model reaction-diffusion system agree qualitatively with the experiment and provide insight into the physical mechanism that drives the observed behavior.

Spatiotemporal patterns in a one-dimensional open reaction-diffusion system

“…The Couette reactor has been modeled recently by Vastano et al [6,14]. The local chemistry of the Couette reactor was modeled by an Oregonator model with two species, bromous acid and the catalyst of the BZ reaction [23].…”

“…The present experiments were conducted for a particular BZ chemistry, but it is conjectured that other chemistries (d), and the spread of the trajectory is due to experimental noise.) (e)-(h) These attractors were constructed from time series for periodic, quasiperiodic, frequency-locked, and chaotic states, respectively, obtained in a numerical simulation of a two-species reaction-diffusion model [6,13,14]; in the model A 0 = 0.020, 0.025, 0.050, and 0.065 M, respectively, and D = 0.078 cm2/s for both species (z = 0.25). The attractors in (a) and (e) are limit cycles; (b) and (f) are 2-tori; (c) and (g) are both frequency locked at a 7 : 5 ratio; and (d) and (h) are strange attractors.…”

“…We have studied transitions in chemical patterns in a simple, well-controlled spatially extended system [6]. The reactor, developed in collaboration with Ouyang et al [8], is a circular Couette system: the reaction occurs in an annular region formed by two concentric cylinders, the inner of which is rotating while the outer one is stationary [6,8,9] #1.…”

“…The reactor, developed in collaboration with Ouyang et al [8], is a circular Couette system: the reaction occurs in an annular region formed by two concentric cylinders, the inner of which is rotating while the outer one is stationary [6,8,9] #1. Reagents are fed and removed at each end of the annulus; the flow rates are carefully adjusted so that there is no net mass flux in the axial direction.…”

Spatial patterns in a uniformly fed membrane reactor

“…One type has an imposed chemical gradient, as in the two-dimensional ring-shaped reactor of Noszticzius et al [5] and Kreisberg et al [6], and in the effectively one-dimensional Couette reactor developed in Austin [7] and Bordeaux [8]. A second type of reactor has a uniform diffusive feed orthogonal to the line or plane in which a pattern forms.…”