Commun. Comput. Phys., 9 (2011), pp. 1081-1093.

Enslaved Phase-Separation Fronts and Liesegang Pattern Formation

E. M. Foard 1*, A. J. Wagner 1

1 Department of Physics, North Dakota State University, Fargo, ND 58105, USA.

Received 10 November 2009; Accepted (in revised version) 2 September 2010
Available online 24 December 2010


We show that an enslaved phase-separation front moving with diffusive speeds $U=C/\sqrt{T}$ can leave alternating domains of increasing size in their wake. We find the size and spacing of these domains is identical to Liesegang patterns. For equal composition of the components we are able to predict the exact form of the pattern analytically. To our knowledge this is the first fully analytical derivation of the Liesegang laws. We also show that there is a critical value for C below which only two domains are formed. Our analytical predictions are verified by numerical simulations using a lattice Boltzmann method.

AMS subject classifications: 35B36, 65Z05, 74S30, 76T99

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Key words: Liesegang, phase separation, front, reaction diffusion, pattern formation, lattice Boltzmann, Matalon-Packter.

*Corresponding author.
Email: (E. M. Foard), (A. J. Wagner)

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