The Tricky Water Energy Budget of Freezing Soil: A Thermodynamic Framework for Understanding Phase Changes

Abstract

Freezing soil presents unique challenges in understanding the coupled mass and energy dynamics within the Earth’s critical zone. This paper focuses on the thermodynamic energy budget of pore water within a rigid soil skeleton, and presents a thermodynamic framework for analysing phase transitions in soil–water-ice systems. Three elements, so far treated separately in the hydrological, geotechnical and physical-chemistry literatures, are assembled here into a single self-consistent chain: (i) a unified derivation of freezing point depression integrating capillary (Gibbs-Thomson), osmotic, and adsorptive mechanisms through a single chemical-potential decomposition; (ii) an explicit thermodynamic derivation of the Soil Freezing Characteristic Curve (SFCC) from the Soil Water Retention Curve (SWRC) via the generalised Clausius-Clapeyron relation, incorporating Lu’s adsorption-aware retention model; and (iii) the connection of the SFCC to a Darcy-scale enthalpy balance as a constitutive closure. Temperature, pressure and chemical potential act as the driving forces, but every constitutive relation derived here assumes local thermodynamic equilibrium within each representative elementary volume, i.e., the framework is non-equilibrium at the Darcy scale and equilibrium at the pore scale. Rate-dependent behaviour is identified as an open problem, not resolved. The framework accounts for freezing point depression through mechanisms including the Gibbs-Thomson effect, solute presence, ice nucleation, and surface interactions. We demonstrate how upscaling from pore-scale thermodynamics to the Darcy scale introduces theoretical challenges in determining phase transformation rates and flux laws. The sequential freezing process, governed by water energetic states in different pore sizes, creates complex interplay between capillary forces and phase changes essential for modeling permafrost dynamics and seasonal freeze-thaw cycles. The contribution is theoretical as no new measurements are reported, and quantitative validation against measured soil freezing characteristic curves is deferred to a companion paper. The framework rests on three assumptions: local equilibrium, instantaneous redistribution of water within a representative elementary volume, and the “freezing = drying” analogy. Each is therefore stated explicitly, together with the conditions under which it is expected to fail.