Abstract
Subcooled water is the primordial matrix for ice embryo formation by homogeneous and heterogeneous nucleation. The knowledge of the specific Gibbs free energy and other thermodynamic quantities of subcooled water is one of the basic prerequisites of the theoretical analysis of ice crystallization in terms of classical nucleation theory. The most advanced equation of state of subcooled water is the IAPWS G12-15 formulation. The determination of the thermodynamic quantities of subcooled water on the basis of this equation of state requires the iterative determination of the fraction of low-density water in the two-state mixture of low-density and high-density subcooled water from a transcendental equation. For applications such as microscopic nucleation simulation models requiring highly frequent calls of the IAPWS G12-15 calculus, a new two-step predictor-corrector method for the approximative determination of the low-density water fraction has been developed. The new solution method allows a sufficiently accurate determination of the specific Gibbs energy and of all other thermodynamic quantities of subcooled water at given pressure and temperature, such as specific volume and mass density, specific entropy, isothermal compressibility, thermal expansion coefficient, specific isobaric and isochoric heat capacities, and speed of sound. The misfit of this new approximate analytical solution against the exact numerical solution was demonstrated to be smaller than or equal to the misprediction of the original IAPWS G12-15 formulation with respect to experimental values.
Highlights
The knowledge of the properties of supercooled or subcooled water is of outstanding importance for a variety of natural and technical processes related to phase transitions of water such as the microphysical evolution of atmospheric clouds, the cryopreservation of organelles, cells, tissues, extracellular matrices, organs, and foods; and water vitrification.Subcooled water is the primordial matrix for ice embryo formation by homogeneous and heterogeneous nucleation
On this basis the differences between the traditional numerical and the new analytical solution of the mole fraction of subcooled water together with the thermodynamic deliveries of the IAPWS G12-15 [36] formulation are determined as functions of pressure and temperature, such as the specific Gibbs energy, the specific volume and mass density, the specific entropy, the isothermal compressibility, the thermal expansion coefficient, the specific isobaric and isochoric heat capacities, and speed of sound
On the base of the results presented in Section SM-5, Table SM-5.1, one can state the correct implementation of the numerical solver of the IAPWS G12-15 [36] formulation
Summary
Subcooled water is the primordial matrix for ice embryo formation by homogeneous and heterogeneous nucleation. Hellmuth et al [22] studied the variation of the homogeneous freezing rate of subcooled water in dependence on pressure and temperature. Entropy 2020, 22, 933 water–ice system were scaled in terms of fundamental thermodynamic properties of the macrophases of subcooled water and hexagonal ice, such as the Gibbs energy, entropy, enthalpy, mass density, isobaric heat capacity, isothermal compressibility, and isobaric thermal expansivity. These quantities appeared the generating ones for the determination of the nucleation metrics.
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