Consequences of fluctuations in Liesegang pattern formation

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