Ostwald ripening in Two Dimensions: Correlations and Scaling Beyond Mean Field

TL;DR

This paper develops a quasi-mean field model for Ostwald ripening in two dimensions, capturing correlations and scaling behaviors beyond traditional mean-field approaches, and validates it against experimental data.

Contribution

It introduces a novel quasi-mean field model with pairwise interactions for 2D Ostwald ripening, extending beyond mean-field approximations.

Findings

Good agreement with experimental correlation functions

Numerical solutions for large droplet systems

Model captures dynamics beyond mean-field theory

Abstract

We present a systematic quasi-mean field model of the Ostwald ripening process in two dimensions. Our approach yields a set of dynamic equations for the temporal evolution of the minority phase droplets' radii. The equations contain only pairwise interactions between the droplets; these interactions are evaluated in a mean- field type manner. We proceed to solve numerically the dynamic equations for systems of tens of thousands of interacting droplets. The numerical results are compared with the experimental data obtained by Krichevsky and Stavans for the relatively large volume fraction $\phi=0.13$. We found good agreement with experiment even for various correlation functions.