Coarsening Dynamics for the Convective Cahn-Hilliard Equation
Stephen J. Watson, Felix Otto, Boris Y. Rubinstein, and Stephen H. Davis
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Submission date: 22. Apr. 2002
published in: Physica / D, 178 (2003) 3-4, p. 127-148
DOI number (of the published article): 10.1016/S0167-2789(03)00048-4
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We characterize the coarsening dynamics associated with a convective Cahn-Hilliard equation in one space dimension. First, we derive a sharp-interface theory based on a quasi-static matched asymptotic analysis. Two distinct types of discontinuity (kink and anti-kink) arise due to the presence of convection, and their motions are governed to leading order by a nearest-neighbors interaction dynamical system. Numerical simulations of the kink/anti-kink dynamics display marked self-similarity in the coarsening process, and reveal a pinching mechanism, identified through a linear stability analysis, as the dominant coarsening event. A self-similar period-doubling pinching ansatz is proposed for the coarsening process, and an analytical coarsening law, valid over all length scales, is derived. Our theoretical predictions are in good agreement with numerical simulations that have been performed both on the sharp-interface model and the original PDE.