Eur. Phys. J. B 29, 305-309 (2002)
https://doi.org/10.1140/epjb/e2002-00306-7

Non-linear dynamics of spinodal decomposition

¹ Centre de Physique Moléculaire Optique et Hertzienne, Université Bordeaux I, 33406 Talence Cedex, France
² Laboratoire de Modélisation en Mécanique (UMR CNRS 7607) , Université Pierre et Marie Curie, 8 rue du Capitaine Scott, 75015 Paris, France

Corresponding author: ^a josseran@lmm.jussieu.fr

Received: 16 October 2001
Revised: 15 March 2002
Published online: 2 October 2002

Abstract

We develop a new technique describing the non linear growth of interfaces. We apply this analytical approach to the one dimensional Cahn-Hilliard equation. The dynamics is captured through a solvability condition performed over a particular family of quasi-static solutions. The main result is that the dynamics along this particular class of solutions can be expressed in terms of a simple ordinary differential equation. The density profile of the stationary regime found at the end of the non-linear growth is also well characterized. Numerical simulations are compared in a satisfactory way with the analytical results through three different fitting methods and asymptotic dynamics are well recovered, even far from the region where the approximations hold.