Abstract
Our purpose is to start understanding from a mathematical viewpoint experiments in which regularized structures with spatially distinct bands or rings of precipitated material are exhibited, with clearly visible scaling properties. Such patterns are known as Liesegang bands or rings. In this paper, we study a one-dimensional version of the Keller and Rubinow model and present conditions ensuring the existence of Liesegang bands.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Hilhorst, D., van der Hout, R., Peletier, L.A.: The fast reaction limit for a reaction-diffusion system. J. Math. Anal. Appl. 199, 349–373 (1996)
Hilhorst, D., van der Hout, R., Peletier, L.A.: Diffusion in the presence of fast reaction: the case of a general monotone reaction term. J. Math. Sci. Univ. Tokyo 4, 469–517 (1997)
Kai, S.: Private communications (2006)
Kai, S., Muller, S.C.: Spatial and temporal macroscopic structures in chemical reaction system: precipitation patterns and interfacial motion. Sci. Form 1, 8–38 (1985)
Keller, J.B., Rubinow, S.I.: Recurrent precipitation and Liesegang rings. J. Chem. Phys. 74, 5000–5007 (1981)
Liesegang, R.E.: Chemische Fernwirkung. Photo. Archiv 800, 305–309 (1896)
Mimura, M., Ohnishi, I., Ueyama, D.: A mathematical aspect of Liesegang phenomena in two space dimensions. Res. Rep. Res. Inst. Math. Sci. 1499, 185–201 (2006)
Ohnishi, I., Mimura, M.: A mathematical aspect of Liesegang phenomena. In: Proceedings of Equadiff-11, pp. 343–352 (2005)
Smith, D.: On Ostwald’s supersaturation theory of rhythmic precipitation (Liesegang’s rings). J. Chem. Phys. 81, 3102–3115 (1984)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Hilhorst, D., van der Hout, R., Mimura, M. et al. A Mathematical Study of the One-Dimensional Keller and Rubinow Model for Liesegang Bands. J Stat Phys 135, 107–132 (2009). https://doi.org/10.1007/s10955-009-9701-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10955-009-9701-9