In 1896, colloid-chemist R.E. Liesegang [4] observed strikingly regular patterns in precipitation-reaction processes, which are referred to as Liesegang bands or rings, according to their shape. In this talk I introduce an attempt to understand from a mathematical viewpoint the experiments in which regularized structures with spatially distinct bands of precipitated material are exhibited, with clearly visible scaling properties. This study is a result [1] of a collaboration with Professors D. Hilhorst, R. van der Hout, and M. Mimura.

References:

• [1] Hilhorst, D., van der Hout, R., Mimura, M., and Ohnishi, I.: A Mathematical Study of the One-Dimensional Keller and Rubinow Model for Liesegang Bands. J. Stat Phys 135: pp. 107-132 (2009)

• [2] Kai, S., Muller, S.C.: Spatial and temporal macroscopic structures in chemical reaction system: precipitation patterns and interfacial motion. Sci. Form 1, pp. 8-38 (1985)

• [3] Keller, J.B., Rubinow, S.I.: Recurrent precipitation and Liesegang rings. J. Chem. Phys. 74, pp. 5000-5007 (1981)

• [4] Liesegang, R.E.: Chemische Fernwirkung. Photo. Archiv 800, pp. 305-309 (1896)

• [5] Mimura, M., Ohnishi, I., Ueyama, D.: A mathematical aspect of Liesegang phenomena in two space dimensions. Res. Rep. Res. Inst. Math. Sci. 1499, pp. 185-201 (2006)

• [6] Ohnishi, I.,Mimura, M.: A mathematical aspect of Liesegang phenomena. In: Proceedings of Equadiff-11, pp. 343-352 (2005).

• [7] Ohnishi,I. : A mathematical aspect for Liesegang phenomena, Res. Rep. Res. Inst. Math. Sci. 1356, pp. 1-26 (2004).

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