Abstract
A microscopic approach to the formation of Liesegang patterns, based on a cellular automata model, is presented. This approach gives a consistent description of several types of patterns observed experimentally (bands, rings, and spirals). Quantitative predictions are made about the generic laws (time, spacing, and width laws) governing the formation of these patterns. Emphasis is put on the role played by the fluctuations in such nonequilibrium systems.
Similar content being viewed by others
References
M. Bramson and J. Lebowitz,J. Stat. Phys. 62:297 (1991).
S. Cornell, M. Droz, and B. Chopard,Physica A 188:322 (1992).
S. Cornell, M. Droz, and B. Chopard,Phys. Rev. A 44:4826 (1991).
S. Cornell and M. Droz,Phys. Rev. Lett. 70:3824 (1993).
Nonequilibrium Chemical Dynamics: From Experiment to Microscopic Simulations,Physica 188:1–468 (1992).
M. Droz and L. Frachebourg,Helv. Phys. Acta 66:97 (1993).
B. Chopard, S. Cornell, M. Droz, and L. Frachebourg, inCellular Automata: Prospects in Astrophysical Applications, J. M. Perdang and A. Lejeune, eds. (World Scientific, Singapore, 1993), pp. 157–186.
D. Dab, J.-P. Boon, and Y.-X. Li,Phys. Rev. Lett. 66:2535 (1991).
R. Kapral, A. Lawniczak, and P. Masiar,Phys. Rev. Lett. 66:2539 (1991).
K. Jablczynski,Bull. Soc. Chim. Fr. 33:1592 (1923).
R. E. Liesegang,Naturwiss. Wochenschr. 11:353 (1896).
R. E. Liesegang,Photog. Arch. 21:221 (1896).
L. Gálfi and Z. Rácz,Phys. Rev. A 38:3151 (1988).
H. K. Henisch,Periodic Precipitation (Pergamon Press, 1991).
B. Mathur and S. Ghosh,Kolloid-Z. 159:143 (1958).
S. Prager,J. Chem. Phys. 25:279 (1956).
Ya. B. Zeldovitch, G. I. Barrenblatt, and R. L. Salganik,Sov. Phys. Dokl. 6:869 (1962).
D. A. Smith,J. Phys. Chem. 81:3102 (1984).
G. T. Dee,Phys. Rev. Lett. 57:275 (1986).
M. E. Le Van and J. Ross,J. Phys. Chem. 91:6300 (1987).
W. Ostwald,Lehrbuch der allgemeinen Chemie (Engelman, Leipzig, 1897).
B. Chopard, P. Luthi, and M. Droz,Phys. Rev. Lett.,72:1384 (1994).
T. A. Witten, inOn Growth and Form, H. E. Stanley and N. Ostrowsky, eds. (Martinus Nijhoff, 1985), p. 54.
B. Chopard and M. Droz,J. Stat. Phys. 64:859 (1991).
J. Nittmann and H. E. Stanley,J. Phys. A 20:L1185 (1987).
R. Benzi, S. Succi, and M. Vergassola,Physics Reports 222:145 (1992).
K. M. Pillai, V. K. Vaidyan, and M. A. Ittyachan,Colloid Polymer Sci. 258:831 (1980).
B. Chopard, H. J. Herrmann, and T. Vicsek,Nature 353:409 (1991).
I. Sunagawa,Bull. Mineral. 104:81 (1981).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Chopard, B., Luthi, P. & Droz, M. Microscopic approach to the formation of Liesegang patterns. J Stat Phys 76, 661–677 (1994). https://doi.org/10.1007/BF02188680
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02188680