Creation of Clusters via a Thermal Quench

TL;DR

This paper models the nucleation and growth of clusters during a slow vapor cooling process, using asymptotic methods to solve a differential equation and analyze cluster size distribution and total cluster formation.

Contribution

It introduces a novel mathematical approach to describe cluster formation during a thermal quench using asymptotic analysis and differential equations.

Findings

Distribution of cluster sizes after quench characterized

Total number of clusters generated quantified

Chemical potential dynamics during nucleation modeled

Abstract

The nucleation and growth of clusters in a progressively cooled vapor is studied. The chemical-potential of the vapor increases, resulting in a rapidly increasing nucleation rate. The growth of the newly created clusters depletes monomers, and counters the increase in chemical-potential. Eventually, the chemical potential reaches a maximum and begins to decrease. Shortly thereafter the nucleation of new clusters effectively ceases. Assuming a slow quench rate, asymptotic methods are used to convert the non-linear advection equation of the cluster-size distribution into a fourth-order differential equation, which is solved numerically. The distribution of cluster-sizes that emerges from this creation era of the quench process, and the total amount of clusters generated are found.