Cross-diffusion and pattern formation in reaction–diffusion systems

Abstract

Cross-diffusion, the phenomenon in which a gradient in the concentration of one species induces a flux of another chemical species, has generally been neglected in the study of reaction-diffusion systems.We summarize experiments that demonstrate that cross-diffusion coefficients can be quite significant, even exceeding ''normal,'' diagonal diffusion coefficients in magnitude in systems that involve ions, micelles, complex formation, excluded volume effects (e.g., surface or polymer reactions) and other phenomena commonly encountered in situations of interest to chemists. We then demonstrate with a series of model calculations that cross-diffusion can lead to spatial and spatiotemporal pattern formation, even in relatively simple systems. We also show that, in the absence of cross-diffusion among the reacting species, introduction of a nonreactive species that induces appropriate cross-diffusive fluxes with reactive species can lead to pattern formation.

Spectromicroscopy of pulses transporting alkali metal in a surface reaction

“…Formally, diffusion is here no longer Fickian and mass transport is controlled by a gradient in the chemical potential. 7,8 Such patterns are often referred to as the result of a ''reactive phase separation''. [4][5][6] On catalytic surfaces, they have been first observed in the K-promoted Rh(110) and, later, on a Rh(110) surface alloyed with Pd/Au, both systems being exposed to the O 2 + H 2 reaction.…”

Model of the Belousov-Zhabotinsky Reaction

“…At the limit g/maxState → 0, we are likely to obtained a uniform intensity. It shows the unsuitability of the reaction-diffusion model for the description of the B-Z reaction [6]. …”

“…Until recently, the reaction-diffusion simulations based on PDEs, which are central models of chemical processes, have been used extensively to explain the self-organizing Belousov-Zhabotinsky reaction [6]. This kind of simulation expects an instantaneous chemical change.…”

High-Entropy Alloys: A Current Evaluation of Founding Ideas and Core Effects and Exploring “Nonlinear Alloys”

“…27 This occurs when the presence of one element changes the chemical potential of other elements in the alloy. 28 Tsai et al assumed that cross terms are negligible to facilitate analysis, and Kulkarni and Chauhan evaluate interdiffusion in CoCrFeNi to explore this assumption.…”