Regular Liesegang patterns and precipitation waves in an open system

Abstract

We investigate the regular and moving Liesegang pattern formation phenomena in an open system. First, simulations have been performed at fixed coupling between the reactive medium and the reservoir, later this control parameter was varied during the simulations resulting in various phenomena. We predicted and monitored for the first time various--dynamically changing--precipitation structures and a spatial hysteresis phenomenon, which is beyond the scope of the Turing instability. The dynamics of the reaction is well detectable using specific quantities: the total amount of precipitate and its center of gravity.

Pattern Formation in Precipitation Reactions: The Liesegang Phenomenon

“…In these systems, the chemical process consists of two steps: (i) precipitation, A (aq) + B (aq) → P (s) and (ii) complex formation/dissolution of the precipitate in an excess of A­(aq), P(s) + A­(aq) → complex­(aq), where A­(aq), B­(aq), and P(s) are the outer and inner electrolytes and the precipitate, respectively. A combination of this type of reaction with the diffusion of the reagents in a Liesegang-type experimental setup provides a seemingly moving precipitation zone or a set of bands traveling farther from the junction point (gel surface) of the electrolytes (Figure e). , These systems are the following: (i) cobalt hydroxide (Co 2+ (aq) + 2OH – (aq) → Co­(OH) 2 (s), Co­(OH) 2 (s) + 6NH 3 → [Co­(NH 3 ) 6 ] 2+ (aq)); − (ii) aluminum hydroxide (Al 3+ (aq)+ 3OH – (aq) → Al­(OH) 3 (s), Al­(OH) 3 (s) + OH – (aq) → [Al­(OH) 4 ] − (aq)); , and (iii) mercuric iodide (Hg 2+ (aq) + 2I – (aq) → HgI 2 (s), HgI 2 (s) + 2I – (aq) → [HgI 4 ] 2– (aq)) . In a precipitation–dissolution system, the deterministic chaotic variation of the number of the bands in time was reported …”

Propagating Fronts and Morphological Instabilities in a Precipitation Reaction

“…However, numerical simulations on a redissolution reaction performed in an open system, where a continuous supply of only the inner electrolyte allows the appearance of moving Liesegang patterns, have been predicted by Lagzi and Izsak. 22 In this article, we demonstrate lateral precipitation pattern formation in the NaOH/AlCl 3 redissolution system, at the meeting of counterpropagating fronts of the electrolytes. We use a disc-shaped two-side-fed gel reactor (Figure 1), where the axial extension (w) is significantly smaller than the lateral one (d).…”

“…This model has been used by Lagzi and Izsaḱ to simulate a moving Liesegang pattern in an open system. 22 For simplicity, we studied the 1D dynamics of the model along a coordinate x, which corresponds to the axial direction in the reactor. At the boundaries, Dirichlet boundary conditions were applied, according to the presence of the continuously refilled tanks at the opposite sides of the gel (Figure 1).…”

“…The development of stationary precipitation rings was observed in the K 2 CrO 4 /Cu­(NO 3 ) 2 reaction in a two-side-fed gel reactor with an annular-shaped gel, where the gel is fed on its inner and outer rims and the axial extension of the gel was 5 times larger than the lateral one. However, numerical simulations on a redissolution reaction performed in an open system, where a continuous supply of only the inner electrolyte allows the appearance of moving Liesegang patterns, have been predicted by Lagzi and Izsak …”

Comparison of models and lattice-gas simulations for Liesegang patterns

“…Alternative geometries [35] and complex 3d boundary conditions [2,3,36] have been studied experimentally. Variation of the reaction terms [37], additional terms for a dissolution of the bands [15,38], as well as open systems [39] and, last but not least, systems with an additional electric field [15,40,41,42] have been studied to vary the patterns. In very recent work the motion of the reaction front is even detached from the phase separation, which might be initiated, e. g., by a temperature gradient [43].…”