Diffusive Instabilities and Chemical Reactions

Abstract

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.

On the projection of functions invariant under the action of a crystallographic group

“…The results in this article were motivated by the study of patterns in reactiondiffusion experiments on thin layers, where the observation method carries information from the depth of a layer and thus corresponds to a projection whose role in the formation of a pattern is not always clear (see Gomes [10] , De Kepper et al [6], Borckmans et al [2] and other articles by the same authors). Our results are a first step in an attempt to clarify this issue.…”

“…Moreover, there is an element (0, a) ∈ L, with a = 0, due to the existence of σ in J, (see properties (2) and (3) of Lemma 5.2), and thus M * y0 ∩ N * σ = ∅. Supposek ∈ M * y0 − P * and k = (0, 0).…”

Front propagation in infinite cylinders. II. The sharp reaction zone limit

“…We note that, although the derivation is done in the context of a thermodiffusional model of combustion [9,14,28], similar modeling is applicable in a wider context, in particular, in the case of chemical reactions in gel reactors (see e.g., [8]). Let us recall briefly the thermodiffusional model of laminar flames.…”

Spatio-temporal organization in a morphochemical electrodeposition model: Hopf and Turing instabilities and their interplay

“…Turing patterns in a chemical reactor were first experimentally observed by De Kepper's group in a chlorite-iodide-malonic acid (CIMA) reaction [18] and later confirmed by Ouyang and Swinney who observed striped as well as spotty patterns [53]. The chance to experimentally detect Turing structures has produced a renewed interest in these systems as shown by the large number of theoretical [35,58], computational [43,44,67] and experimental studies in the field [6,42,52].…”