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.