A maximum-entropy approach to the adiabatic freezing of a supercooled liquid

TL;DR

This paper uses a maximum-entropy approach combined with van der Waals theory to analyze the adiabatic freezing of supercooled liquids, focusing on the effects of constraints and foreign gases on solidification.

Contribution

It introduces a novel application of maximum-entropy methods to quantify solidification in supercooled liquids under various constraints and conditions.

Findings

Solidification often initiates near the container wall under certain conditions.

The presence of foreign gas influences the fraction of liquid that solidifies.

Energy costs of droplet formation depend on thermal and mechanical insulation.

Abstract

I employ the van der Waals theory of Baus and coworkers to analyze the fast, adiabatic decay of a supercooled liquid in a closed vessel with which the solidification process usually starts. By imposing a further constraint on either the system volume or pressure, I use the maximum-entropy method to quantify the fraction of liquid that is transformed into solid as a function of undercooling and of the amount of a foreign gas that could possibly be also present in the test tube. Upon looking at the implications of thermal and mechanical insulation for the energy cost of forming a solid droplet within the liquid, I identify one situation where the onset of solidification inevitably occurs near the wall in contact with the bath.