The generalized Clapeyron equation and its application to confined ice growth

TL;DR

This paper extends the classical Clapeyron equation to anisotropic stresses and higher-order terms, improving its applicability to confined ice growth and related stress-induced phenomena.

Contribution

It provides a rigorous derivation of the generalized Clapeyron equation, including conditions for validity and extensions for anisotropic stresses and higher-order effects.

Findings

Extended the Clapeyron equation to anisotropic stress states.

Identified material property-dependent validity ranges.

Validated extended model with experimental data on ice pressure melting.

Abstract

Most theoretical descriptions of stresses induced by freezing are rooted in the (generalized) Clapeyron equation, which predicts the pressure that a solid can exert as it cools below its melting temperature. This equation is central for topics ranging beyond glaciology to geomorphology, civil engineering, food storage, and cryopreservation. However, it has inherent limitations, requiring isotropic solid stresses and conditions near bulk equilibrium. Here, we examine when the Clapeyron equation is applicable by providing a rigorous derivation that details all assumptions. We demonstrate the natural extension for anisotropic stress states, and we show how the temperature and pressure ranges for validity depend on well-defined material properties. Finally, we demonstrate how the range of applicability of the (linear) Clapeyron equation can be extended by adding higher-order terms, yielding results that are in good agreement with experimental data for the pressure melting of ice.