Expressions for the Evaporation and Condensation Coefficients in the Hertz-Knudsen Relation

Although the Hertz-Knudsen (HK) relation is often used to correlate evaporation data, the relation contains two empirical parameters (the evaporation and condensation coefficients) that have inexplicably been found to span 3 orders of magnitude. Explicit expressions for these coefficients have yet to be determined. This review will examine sources of error in the HK relation that have led to the coefficients' scatter. Through an examination of theoretical, experimental, and molecular dynamics simulation studies of evaporation, this review will show that the HK relation is incomplete, since it is missing an important physical concept: the coupling between the vapor and liquid phases during evaporation. The review also examines a modified HK relation, obtained from the quantum-mechanically based statistical rate theory (SRT) expression for the evaporation flux and applying a limit to it in which the thermal energy is dominant. Explicit expressions for the evaporation and condensation coefficients are defined in this limit, with the surprising result that the coefficients are not bounded by unity. An examination is made with 127 reported evaporation experiments of water and of ethanol, leading to a new physical interpretation of the coefficients. The review concludes by showing how seemingly small simplifications, such as assuming thermal equilibrium across the liquid vapor interface during evaporation, can lead to the erroneous predictions from the HK relation that have been reported in the literature.