Late-stage coarsening for off-critical quenches: Scaling functions and the growth law

Abstract

We carry out a detailed numerical study of the Cahn-Hilliard equation in two dimensions for phase separation in very large systems and for different values of the area fraction \ensuremath{\varphi}. We present results for the scaling function obtained from the pair-correlation function, the structure factor, and the droplet distribution function. We find that dynamical scaling is satisfied at late times for all of the above functions and for different area fractions. We study how the shape of these scaling functions changes with the area fractions and compare these results with available theoretical predictions. We have also analyzed the growth law for the characteristic domain size for various area fractions. Our analysis of the time dependence of various measures for the characteristic length supports a modified Lifshitz-Slyozov law in which the asymptotic-growth-law exponent is 1/3 for all area fractions.