Theory of Ostwald ripening for two-dimensional systems

A modified theory of late-stage phase separation in two dimensions is presented. We show that direct correlation between two droplets, ignored in an earlier theory, significantly changes the droplet size distribution function even at very low area fraction, although it does not affect the asymptotic droplet growth power law $t^{1/3}$. In the low-area-fraction limit this correlation effect leads to a logarithmic correction term which is larger than any other effects. We also show that there is no finite cutoff for the scaled distribution function due to the associated second-order differential equation.