2019/11/08 by Náraigh, Lennon Ó, Gloster, Andrew
#Computational Physics (physics.comp-ph) #FOS: Physical sciences
paper · doi:10.48550/arxiv.1911.03386
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 Lifshitz--Slyozov--Wagner model. We also look at the Cahn--Hilliard equation with constant mobility. We define the coarsening rate as β=-(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 long-time average value of β should not exceed 1/3 -- this result is summarized here as ⟨ β⟩≤ 1/3. We explore this conjecture for the two considered models. Using large-scale 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 β. Our results show that the droplet population model and the Cahn--Hilliard equation (asymmetric mixtures) are demonstrably in agreement with ⟨β⟩≤ 1/3. The results for the Cahn--Hilliard equation in the case of symmetric mixtures show ⟨β⟩ sometimes exceeds 1/3 in our simulations. However, the possibility is left open for the very long-time average values of ⟨ β⟩ 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. \endabstract