Binary nucleation rates for ethanol/water mixtures in supersonic Laval nozzles: Analyses by the first and second nucleation theorems

Abstract

We performed pressure trace measurements and small angle x-ray scattering measurements to determine the vapor-liquid nucleation rates of EtOH/H2O mixtures including pure EtOH and pure H2O in two supersonic Laval nozzles with different expansion rates. The nucleation rates varied from 0.9 × 10(17) to 16 × 10(17) cm(-3) s(-1) over the temperature range of 210 K to 230 K, EtOH activity range of 0 to 11.6, and H2O activity range of 0 to 124. The first and second nucleation theorems were applied to the nucleation rates to estimate the sizes, compositions, and excess energies of the critical clusters. The critical clusters contained from 4 to 15 molecules for pure H2O and EtOH/H2O clusters, and from 16 to 23 molecules for pure EtOH clusters. Comparing the excess energies of the pure H2O critical clusters with the results of a quantum-chemistry calculation suggested that the pre-factor of the theoretical nucleation rate is almost constant regardless of the monomer concentration. One possible explanation for this result is that cooling of the critical clusters limits the nucleation rate under the highly supersaturated conditions. The results of the analyses also yielded the relation between the surface energy and the composition of the critical clusters, where the latter are predicted to consist only of surface molecules. Applying this relationship to the EtOH/H2O bulk liquid mixtures, we estimated the EtOH mole fraction in the surface layer and found it is higher than that derived from the surface tension based on the Gibbs adsorption equation when the EtOH mole fraction in the liquid is higher than about 0.2 mol/mol. This discrepancy was attributed to the existence of the EtOH depletion layer just below the surface layer of the liquid.