Commun. Comput. Phys., 10 (2011), pp. 867-881.


Transition of Liesegang Precipitation Systems: Simulations with an Adaptive Grid PDE Method

Paul A. Zegeling 1, Istvan Lagzi 2, Ferenc Izsak 3*

1 Department of Mathematics, Utrecht University, P.O. Box 80010, 3508 TA Utrecht, The Netherlands.
2 Department of Meteorology, Eotvos University, H-1117 Budapest, Pazmany setany 1/A, Hungary.
3 Department of Applied Analysis and Computational Mathematics, Eotvos University, H-1117 Budapest, Pazmany setany 1/C, Hungary; and Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands.

Received 5 May 2010; Accepted (in revised version) 3 December 2010
Available online 13 June 2011
doi:10.4208/cicp.050510.031210a

Abstract

The dynamics of the Liesegang type pattern formation is investigated in a centrally symmetric two-dimensional setup. According to the observations in real experiments, the qualitative change of the dynamics is exhibited for slightly different initial conditions. Two kinds of chemical mechanisms are studied; in both cases the pattern formation 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 computationally 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.

AMS subject classifications: 65N50, 65M50, 35B36

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Key words: Liesegang phenomenon, numerical simulations, adaptive grid technique.

*Corresponding author.
Email: p.a.zegeling@uu.nl (P. A. Zegeling), lagzi@nimbus.elte.hu (I. Lagzi), izsakf@cs.elte.hu (F. Izsak)
 

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