A largescale statistical study of the coarsening rate in models of OstwaldRipening
Abstract
In this article we look at the coarsening rate in two standard models of Ostwald Ripening. Specifically, we look at a discrete droplet population model, which in the limit of an infinite droplet population reduces to the classical LifshitzSlyozovWagner model. We also look at the CahnHilliard equation with constant mobility. We define the coarsening rate as $\beta=(t/F)(d F/d t)$, where $F$ is the total free energy of the system and $t$ is time. There is a conjecture that the longtime average value of $\beta$ should not exceed $1/3$  this result is summarized here as $\langle \beta\rangle\leq 1/3$. We explore this conjecture for the two considered models. Using largescale computational resources (specifically, GPU computing employing thousands of threads), we are able to construct ensembles of simulations and thereby build up a statistical picture of $\beta$. Our results show that the droplet population model and the CahnHilliard equation (asymmetric mixtures) are demonstrably in agreement with $\langle\beta\rangle\leq 1/3$. The results for the CahnHilliard equation in the case of symmetric mixtures show $\langle\beta\rangle$ sometimes exceeds $1/3$ in our simulations. However, the possibility is left open for the very longtime average values of $\langle \beta\rangle$ to be bounded above by $1/3$. The theoretical methodology laid out in this paper sets a path for future more intensive computational studies whereby this conjecture can be explored in more depth. \end{abstract}
 Publication:

arXiv eprints
 Pub Date:
 November 2019
 arXiv:
 arXiv:1911.03386
 Bibcode:
 2019arXiv191103386N
 Keywords:

 Physics  Computational Physics
 EPrint:
 27 pages, 20 figures