On the formation/dissolution of equilibrium droplets

TL;DR

This paper analyzes the conditions under which droplets form or dissolve in liquid-vapor systems at phase coexistence, identifying a universal parameter that determines droplet emergence and describing the universal properties of the initial droplet formation.

Contribution

It introduces a universal dimensionless parameter that predicts droplet formation in phase coexistence systems and extends the analysis to various two-phase systems including solid/gas.

Findings

Droplets form when the parameter exceeds a critical value.

The initial droplet contains a universal fraction of excess particles.

The framework applies to multiple two-phase systems beyond liquids and vapors.

Abstract

We consider liquid-vapor systems in finite volume $V\subset\R^d$ at parameter values corresponding to phase coexistence and study droplet formation due to a fixed excess $\delta N$ of particles above the ambient gas density. We identify a dimensionless parameter $\Delta\sim(\delta N)^{(d+1)/d}/V$ and a \textrm{universal} value $\Deltac=\Deltac(d)$, and show that a droplet of the dense phase occurs whenever $\Delta>\Deltac$, while, for $\Delta<\Deltac$, the excess is entirely absorbed into the gaseous background. When the droplet first forms, it comprises a non-trivial, \textrm{universal} fraction of excess particles. Similar reasoning applies to generic two-phase systems at phase coexistence including solid/gas--where the ``droplet'' is crystalline--and polymorphic systems. A sketch of a rigorous proof for the 2D Ising lattice gas is presented; generalizations are discussed heuristically.