Diffusion-driven instabilities by immobilizing the autocatalyst in ionic systems

Abstract

Spatiotemporal coupling of an autocatalytic chemical reaction between ions with diffusion yields various types of reaction-diffusion patterns. The driving force is short range activation and long range inhibition which can be achieved by selective binding of the autocatalyst even for ions with equal mobility. For Turing and lateral instability, we show that identical charge on the autocatalyst and its counterpart has a stabilizing effect on the base state, while opposite charge on them favors the formation of spatial patterns with reversible binding.

Pattern Formation in the Bromate–Sulfite–Ferrocyanide Reaction

“…Recently, Toth and Horvath have shown theoretically that the effect of the local electric field in a reaction where concentration gradients of ionic species exist might have a significant contribution to pattern development. 39 Especially, opposite charge on the key components, that is, the case in the BSF reaction, leads to a migration flux that favors pattern formation. This influence can be suppressed by adding a conducting salt in large concentration.…”

Pattern Formation in a Model of Inflammation

“…Moreover, the diffusion coefficient of the self-inhibitor should be sufficiently higher than that of the self-activator. It is worth noting, that although this is the general concept for emergence of Turing patterns in the systems with greater number of variables as well [40,41], another possibilities for Turing patterns formation exist in multicomponent systems, that can bypass the requirement of short-range activator and long-range inhibitor [42]. However, this requirement is strictly necessary for two-component systems.…”

Introduction to Focus Issue: Oscillations and Dynamic Instabilities in Chemical Systems: Dedicated to Irving R. Epstein on occasion of his 70th birthday

“…7 This idea is further elaborated in the work of T oth and Horv ath in this issue by immobilizing autocatalysts in ionic systems though selective binding, even for ions with equal mobilities. 21 Turing patterns turned out to be rather peculiar patterns; only two clear examples had been demonstrated until 2009 when the De Kepper group developed an operational design method. 22 In the issue, De Kepper and his co-authors elaborate on the journey of discoveries of Turing patterns in new reaction systems from the perspective of the design method.…”