Consequences of fluctuations in Liesegang pattern formationL. Jahnke and J. W. Kantelhardt
Institut für Physik, Martin-Luther-Universität Halle-Wittenberg - 06099 Halle, Germany, EU
received 20 August 2008; accepted in final form 20 October 2008; published November 2008
published online 21 November 2008
Using lattice-gas simulations we show that Liesegang pattern formation in reaction-diffusion systems on small length scales can be described by a mean-field model, supplemented with three first-order corrections. We find that fluctuations due to thermal motion of the particles and due to impurities in the sample increase the number of Liesegang bands or even initiate patterns not forming without fluctuations. I.e., noise enhances or even induces ordering. Therefore, we suggest that it is possible to tune the number or distance of Liesegang bands by changing the impurities in the sample. Moreover, it might be possible to measure the nucleation threshold when changing the level of impurities in a micro- or nano-scale experimental setting.
82.40.Ck - Pattern formation in reactions with diffusion, flow and heat transfer.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
81.30.Mh - Solid-phase precipitation.
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