Universality in diffusion-controlled nucleation and growth

TL;DR

This paper demonstrates that diffusion-controlled nucleation and growth systems exhibit a universal regime where the droplet size distribution remains invariant under parameter rescaling, with an accurate analytic form derived.

Contribution

It introduces the concept of universality in diffusion-controlled nucleation and provides an analytic expression for the size distribution in this regime.

Findings

Size distribution invariance under parameter rescaling

Analytic form for the droplet size distribution

Universality emerges when Gibbs-Thompson effect is negligible

Abstract

Nucleation and growth is studied in a system undergoing diffusion-controlled condensation under gradual changes in parameters, such as cooling. It is demonstrated that when Gibbs-Thompson effect becomes negligible, the system falls into a universal regime. i.e. the final droplet size distribution remains invariant under certain rescaling of system parameters. An approximate yet very accurate analytic form is obtained for the size distribution function in this regime.