Vincent Holten

Thermodynamics of Supercooled Water

We review the available experimental information on the thermodynamic properties of supercooled water and demonstrate the possibility of modeling these thermodynamic properties on a theoretical basis. We show that by assuming the existence of a liquid-liquid critical point in supercooled water, the theory of critical phenomena can give an accurate account of the experimental thermodynamic-property data up to a pressure of 150 MPa. In addition, we show that a phenomenological extension of the theoretical model can account for all currently available experimental data in the supercooled region, up to 400 MPa. The stability limit of the liquid state and possible coupling between crystallization and liquid-liquid separation are also discussed. It is concluded that critical-point thermodynamics describes the available thermodynamic data for supercooled water within experimental accuracy, thus establishing a benchmark for further developments in this area.

Equation of State for Supercooled Water at Pressures up to 400 MPa

An equation of state is presented for the thermodynamic properties of cold and supercooled water. It is valid for temperatures from the homogeneous ice nucleation temperature up to 300 K and for pressures up to 400 MPa, and can be extrapolated up to 1000 MPa. The equation of state is compared with experimental data for the density, expansion coefficient, isothermal compressibility, speed of sound, and heat capacity. Estimates for the accuracy of the equation are given. The melting curve of ice I is calculated from the phase-equilibrium condition between the proposed equation and an existing equation of state for ice I.

Comparison between solutions of the general dynamic equation and the kinetic equation for nucleation and droplet growth

A comparison is made between two models of homogeneous nucleation and droplet growth. The first is a kinetic model yielding the master equations for the concentrations of molecular clusters. Such a model does not make an explicit distinction between nucleation and droplet growth. The second model treats nucleation and growth separately, fully ignoring stochastic effects, and leads to the continuous general dynamic equation (GDE). Problems in applying the GDE model are discussed. A numerical solution of the kinetic equation is compared with an analytic solution of the GDE for two different cases: (1) the onset of nucleation and (2) the nucleation pulse. The kinetic model yields the thickness of the condensation front in size space as a function of supersaturation and dimensionless surface tension. If the GDE is applied properly, solutions of the GDE and the kinetic equation agree, with the exception of very small clusters, near-critical clusters, and the condensation front.

Comment on the nucleation behavior of supercooled water vapor in helium [J. chem. phys. 117, 5647 (2002)]

In a recent paper Peeters et al. published new experimental data on nucleation rates of water in the temperature range of 200-235 K. They reported about a drastic change in the nucleation rate at 207 K. An error in their experimental procedure has been found. The data of Peeters et al. have been reinterpreted. The jump in nucleation rate disappears and the corrected nucleation rate data are in good agreement with data found by Wolk and Strey with a different experimental facility.

Homogeneous water nucleation and droplet growth in methane and carbon dioxide mixtures at 235 K and 10 bar

Homogeneous nucleation rates and droplet growth rates of water in pure methane and mixtures of methane and carbon dioxide were measured in an expansion wave tube at 235 K and 10 bar. The nucleation rate in pure methane is three orders of magnitude higher than literature nucleation rates of water in low-pressure helium or argon. Addition of carbon dioxide to the carrier gas mixture increases the rates even more. Specifically, rates in a mixture of methane and 3% carbon dioxide are a factor of 10 higher than the rates in pure methane. With 25% carbon dioxide, the rates are four orders of magnitude higher than the rates in pure methane. An application of the nucleation theorem shows that the critical cluster consists of 22 water molecules and 5 methane molecules, for nucleation in pure methane. Growth rates of water droplets were measured in methane and in methane-carbon dioxide mixtures at 243 K and 11.5 bar. At equal temperature, pressure and water vapor fraction, the growth rate of the squared droplet radius is about 20% lower in the mixture with 25% carbon dioxide than in pure methane. The lower growth rate is caused by a smaller diffusion coefficient of water in the mixture with carbon dioxide; the difference of the diffusion coefficients is qualitatively reproduced by the empirical Fuller correlation combined with Blancs law.

Kinetic Theory Applied to Nucleation and Droplet Growth

Condensation of liquid from the vapour phase has been studied by the numerical solution of the kinetic equations describing the time dependence of the cluster size distribution. The model has been applied to the nucleation pulse method; the resulting droplet population is investigated. The results are compared with results from a simplified theory that describes nucleation and droplet growth as separate processes. The simulations show that the simplified model is unable to replicate the results of the purely kinetic model.

Response to “Comment on ‘Comparison between solutions of the general dynamic equation and the kinetic equation for nucleation and droplet growth’ ” [J. Chem. Phys. 132, 047101 (2010)]

The analytical results presented in the comment of Shneidman for the droplet size distribution, the thickness of the distribution front, and the location of the stationary source are compared to our earlier numerical results. The agreement is very good in the case of the size distribution and the source location, but the analytical result for the thickness of the front deviates from the numerical result at high supersaturations.

Shock tube problem with phase transition: numerical analysis and experiments

Numerical and experimental studies of phase transition phenomena in a shock tube are presented. The simulations are based on the 2D Euler equations, combined with the extended Hill’s moment method, in which both condensation and evaporation are implemented. Experiments in a pulse-expansion wave tube with water-helium as a test-gas are used to validate the numerical model. Comparing pressure histories and transient properties of the cloud, it is shown that this experimental facilities can be served as an excellent experimental benchmark for numerical methods dealing with phase transition.