Pattern Formation and Self-Organization in a Simple Precipitation System

Abstract

Various types of pattern formation and self-organization phenomena can be observed in biological, chemical, and geochemical systems due to the interaction of reaction with diffusion. The appearance of static precipitation patterns was reported first by Liesegang in 1896. Traveling waves and dynamically changing patterns can also exist in reaction-diffusion systems: the Belousov-Zhabotinsky reaction provides a classical example for these phenomena. Until now, no experimental evidence had been found for the presence of such dynamical patterns in precipitation systems. Pattern formation phenomena, as a result of precipitation front coupling with traveling waves, are investigated in a new simple reaction-diffusion system that is based on the precipitation and complex formation of aluminum hydroxide. A unique kind of self-organization, the spontaneous appearance of traveling waves, and spiral formation inside a precipitation front is reported. The newly designed system is a simple one (we need just two inorganic reactants, and the experimental setup is simple), in which dynamically changing pattern formation can be observed. This work could show a new perspective in precipitation pattern formation and geochemical self-organization.

Protrusion and rising of a gel-based precipitation layer

“…The instability often appears in the interface between a precipitation layer and the surrounding gel. The curvature (or the flatness) of the interface destabilizes, which results in the protrusion of a precipitation region from the interface [7][8][9][10]. The present authors found this type of instability for a counter-diffusion system [11], which was used by Putnis et al [3] to form chemical zoning in particle.…”

“…Recently, macroscopic pattern formation of precipitation layers in gel has attracted much attention. Significant examples are a new type of the Liesegang pattern [10], chemical gardens [9], and a traveling wave [7,8] that appears to be observed for the Belouzov-Zabotinsky reaction.…”

“…The control of crystal growth [1], morphology of inorganic matter [2], and chemical zoning [3][4][5] are examples of the former. The Liesegang pattern [6], a traveling wave [7,8] and chemical gardens [9] are examples of the latter. Recently, macroscopic pattern formation of precipitation layers in gel has attracted much attention.…”

Stochastic cellular automata modeling of excitable systems

“…Spontaneous appearance of travelling waves and spiral formation inside of the precipitation front was thus described for the first time. The dynamics and spatial structure of the observed traveling waves suggest the similar origin of BZ waves and the phenomena in [41]. The result in a real experiment is depicted in Figure 9.…”

“…Pattern formation phenomena in a precipitation system may produce similar structures. Our new experimental investigations [41] have shown the coexistence of precipitation process and excitability without any external forcing. Spontaneous appearance of travelling waves and spiral formation inside of the precipitation front was thus described for the first time.…”