Fast reaction limits and Liesegang bands

By  D. Hilhorst, R. van der Hout, M. Mimura and I. Ohnishi

International Series of Numerical Mathematics, Vol. 154, 241–250

The abstract is the following: 

The purpose of this study is to start understanding from a mathematical viewpoint experiments in which regularized structures with spatially distinct bands and rings of precipitated material were exhibited, with clearly visible scaling properties. This phenomenon has been originally observed by Liesegang [1] in 1896, after whom the name “Liesegang bands/rings” has been coined. Since then there have been a large number of contributions to the understanding of such precipitated pattern formation from experimental as well as theoretical viewpoints. However, as far as we know, there has not been any mathematical study of this problem apart from numerical simulations. In this note we introduce a one-dimensional reaction diffusion system which is a simplified model of the supersaturation model proposed
by Keller and Rubinow [2] in 1981 and study the occurrence of precipitated bands in this system, by means of singular limit analysis.

Fast Reaction Limits and Liesegang Bands

 ©2006 Birkhauser Verlag Basel/Switzerland