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

Published online by Cambridge University Press:  20 August 2015

Paul A. Zegeling,
István Lagzi and
Ferenc Izsák
Paul A. Zegeling*
Affiliation:
Department of Mathematics, Utrecht University, P.O. Box 80010, 3508 TA Utrecht, The Netherlands
István Lagzi*
Affiliation:
Department of Meteorology, Eötvös University, H-1117 Budapest, Pázmány sétány 1/A, Hungary
Ferenc Izsák*
Affiliation:
Department of Applied Analysis and Computational Mathematics, Eötvös University, H-1117 Budapest, Pázmány sétány 1/C, HungaryDepartment of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
*
Email:p.a.zegeling@uu.nl
Email:lagzi@nimbus.elte.hu
Corresponding author.Email:izsakf@cs.elte.hu
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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.

Keywords

65N5065M5035B36Liesegang phenomenonnumerical simulationsadaptive grid technique

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Type
Research Article
Information
Communications in Computational Physics , Volume 10 , Issue 4 , October 2011, pp. 867 - 881
Copyright
Copyright © Global Science Press Limited 2011

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