J. Boissonade

Turing-type chemical patterns in the chlorite-iodide-malonic acid reaction

Abstract We describe experimental observations of symmetry breaking stationary patterns. These patterns are interpreted as the first unambiguous evidence of Turing-type structures in a single-phase isothermal chemical reaction system. Experiments are conducted with the versatile chlorite-iodide-malonic acid reaction in open spatial reactors filled with hydrogel. A phase diagram gathering the domain of existence of symmetry breaking and no-symmetry breaking standing patterns is discussed.

Conventional and unconventional Turing patterns

The formation of two‐dimensional Turing patterns in nonequilibrium chemical systems is studied by numerical simulations with an activator‐substrate depletion model. The relative stabilities of the different hexagonal patterns and the striped patterns are discussed, in particular in the vicinity of the transition, and compared with the present state theory. The generic instabilities of the striped patterns are evidenced. In particular, we report the formation of stable zigzag patterns which share features both of one‐dimensional and two‐dimensional patterns. We also provide examples of temporal evolution in a weakly confined system.

Numerical studies of Turing patterns selection in a two-dimensional system

Abstract The Turing bifurcations of the Schnackenberg model are studied by numerical simulations. The relative stability of the striped and hexagonal patterns are determined for a large range of control parameters. We show that the stability of the triangular and honeycomb forms of hexagonal patterns are exchanged at a critical point. Striped patterns are favoured in the vicinity of this point. We also show that one of the hexagonal phase is reentrant far from the bifurcation point. Finally, we show that striped patterns develop preferentially in directions orthogonal to the walls when no-flux boundary conditions are applied.

Sustained reaction-diffusion structures in an open reactor

Abstract Spontaneous emergence of sustained spatial chemical dissipative structures resulting from only reaction and diffusion processes is a major yet incompletely solved problem in experimental nonlinear dynamics and pattern formation. We introduce a new type of open reactor where both chemical constraints and transport rates are controlled. A sequence of different spatiotemporal reaction -diffusion structures, and most interestingly the first nontrivial stationary pattern, have been obtained by continuous variation of a control parameter with variants of the chlorite-iodide and the Belousov-Zhabotinskii reactions.

Experimental evidence of nucleation induced transition in a bistable chemical system

Abstract It is experimentally shown that a chemical nonequilibrium bistable system presents metastability and stirring rate sensitivity in full agreement with theoretical predictions of nucleation induced transitions.

Sustained patterns in chlorite–iodide reactions in a one‐dimensional reactor

We describe an open one‐dimensional reaction–diffusion system, the Couette reactor, which provides a permanent feed of fresh reactants and simultaneously preserves the diffusion process. Different compositions of variants of chlorite–iodide reactions are fed at both ends, but there is no net axial mass flux in the reactor. The effective diffusion coefficient is the same for all chemical species, and can easily be varied from 10−2 to 1 cm2/s, permitting large size reaction–diffusion structures. Spatial bistability was obtained with the minimal chlorite–iodide reaction in symmetric feed conditions. A larger variety of patterns was observed with the chlorite–iodide–malonic acid reaction and asymmetric feed conditions: a single steady chemical front, two steady fronts, three steady fronts, a single oscillating front, two oscillating fronts, three oscillating fronts, simple colliding fronts, and a bursting pattern. The patterns were studied as a function of several parameters to determine the sequences of bifu...

Theoretical and experimental analysis of phase diagrams and related dynamical properties in the Belousov–Zhabotinskii system

It is shown on the basis of a semiquantitative dynamical analysis and full nonlinear computations that the irreversible Oregonator with flux conditions exhibits a characteristic cross‐shaped phase diagram which expresses the relationships between bistability and periodicity. The results are in good agreement with a whole set of new experiments on the Belousov–Zhabotinskii reaction performed in a continuous stirred tank reactor.

DIFFUSIVE INSTABILITIES AND CHEMICAL REACTIONS

Diffusive instabilities provide the engine for an ever increasing number of dissipative structures. In this class autocatalytic chemical systems are prone to generate temporal and spatial self-organization phenomena. The development of open spatial reactors and the subsequent discovery in 1989 of the stationary reaction–diffusion patterns predicted by Turing [1952] have triggered a large amount of research. This review aims at a comparison between theoretical predictions and experimental results obtained with various type of reactors in use. The differences arising from the use of reactions exhibiting either bistability of homogeneous steady states or a single one in a CSTR are emphasized.

Pattern selection and localized structures in reaction-diffusion systems

We present some theoretical concepts that have been used in the study of chemical disspative structures together with a brief description of recent experimental work on Turing patterns and their interaction with travelling waves.

Turing Patterns: From Myth to Reality

Besides classical equilibrium structures, such as solid state crystals, nature exhibits a number of dissipative structures in systems kept far from equilibrium by permanent driving forces. These structures result from a symmetry breaking instability of the basic thermodynamic state induced by nonlinearities and competition between antagonistic processes [1, 2]. Their archetype is the family of convective instabilities in hydrodynamics [3–4]. Other well-known examples are the homogeneous isothermal chemical systems fed with a permanent flow of fresh reactants which can exhibit oscillating phenomena, provided they encompass appropriate antagonistic catalytic and inhibitory steps [1, 5]. It seems to follow from common sense that introducing molecular diffusion — a transport process which tends to damp any inhomogeinety — should not promote the spontaneous formation of a spatial pattern. However, this naive statement is actually false because, when several species have different diffusion rates, the responses of the antagonistic processes to a local perturbation do not spread at the same rate. As a result, the subtle balance between these processes can break in a nonhomogeneous way. In these conditions, a spatial instability leading eventually to a stationary spatial structure can take place. Although this idea can be tracked down to Rashevsky [6], its modern formulation, published in 1952, is more commonly attributed to Turing [7]. Turing structures were further theorized from the late sixties, in particular by the Brussels group [1, 8, 9], with a progressive introduction of bifurcation theory. Since the basic ingredients — permanent feed, reactions with antagonistic feedbacks, large differences in diffusion coefficients — are common in biological media, the concept has become very popular among a small community of biologists and biomathematicians as a promoter of the early stages of morphogenesis and has initiated a large amount of work in this direction [10–12].