Transition of Liesegang precipitation systems: simulations with an adaptive grid PDE method ∗

The dynamics of the Liesegang type pattern formation is investi-gated in a centrally symmetric two-dimensional setup. According to the observations in real experiments, the qualitative change of the dy-namics is exhibited for slightly different initial conditions. Two kinds of chemical mechanisms are studied; in both cases the pattern forma-tion is described using a phase separation model including the Cahn-Hilliard equations. For the numerical simulations we make use of an adaptive grid PDE method, which successfully deals with the compu-tationally critical cases such as steep gradients in the concentration distribution and investigation of long time behavior. The numerical simulations show a good agreement with the real experiments. ∗P.A. Zegeling would like to acknowledge the support from the Dutch BSIK-projec