2001
DOI: 10.1063/1.1342858
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Formation of Liesegang patterns: Simulations using a kinetic Ising model

Abstract: A kinetic Ising model description of Liesegang phenomena is studied using Monte Carlo simulations. The model takes into account thermal fluctuations, contains noise in the chemical reactions, and its control parameters are experimentally accessible. We find that noisy, irregular precipitation takes place in dimension d=2 while, depending on the values of the control parameters, either irregular patterns or precipitation bands satisfying the regular spacing law emerge in d=3.Comment: 7 pages, 8 ps figures, RevTe Show more

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Cited by 33 publications
(41 citation statements)
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“…This reaction product can further turn into precipitate. [35][36][37] As shown in Figure 3, the diffusion front …”
Section: Results and Discussuionmentioning
confidence: 99%
“…This reaction product can further turn into precipitate. [35][36][37] As shown in Figure 3, the diffusion front …”
Section: Results and Discussuionmentioning
confidence: 99%
“…nucleation thresholds), setting a 0 or b 0 just below such a threshold value might lead to some interesting phenomena. An example of such a complex process is formation of the Liesegang patterns, which are quasiperiodic precipitation patterns emerging in the wake of a mobile chemical reaction front [24,25]. Our study indicates that it should be possible to obtain similar precipitation patterns of species B in reaction-diffusion systems with re- …”
Section: Discussionmentioning
confidence: 73%
“…However, the application of such models to natural systems is hampered by the fact that many parameters may be difficult to estimate, measure or evaluate, in particular those pertaining to the intermediate colloidal phase C. It is thus useful to examine simplified periodic precipitation models that remain qualitatively compatible with more extended models. For example, a reduced mesoscopic description of periodic precipitation phenomena analogous to spinodal decomposition in model B of critical dynamics [17] is available [18,19]. In that interpretation however, the relations between the mesoscopic parameters entering in the field description and the microscopic parameters pertaining to the physics of growth, nucleation and ripening are not clearly established.…”
Section: Introductionmentioning
confidence: 97%