

Preprint 35/2002
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
Pages: 23
published in: Physica / D, 178 (2003) 3-4, p. 127-148
DOI number (of the published article): 10.1016/S0167-2789(03)00048-4
Bibtex
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Abstract:
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.