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.

A series of low-temperature (246 < T(I)(L) < 267 K) steady-state ethanol evaporation experiments have been conducted to determine the saturation vapor pressure of metastable ethanol. The measured interfacial conditions have been used with statistical rate theory (SRT) to develop an expression for the saturation vapor pressure as a function of temperature, f(srt)(eth). This expression is shown to be thermodynamically consistent because it gives predictions of both the evaporative latent heat and the liquid constant-pressure specific heat that are in agreement with independent measurements of these properties. In each experiment, the interfacial vapor temperature was measured to be greater than the interfacial liquid temperature, [triple bond]DeltaT(I)(LV). When f(srt)(eth) is used in SRT to predict DeltaT(I)(LV), the results are shown to be consistent with the measurements. Other expressions for the saturation vapor pressure that are in the literature are examined and found to be thermodynamically inconsistent and do not lead to valid predictions of DeltaT(I)(LV).

Condensation on the nanoscale is essential to understand many natural and synthetic systems relevant to water, air, and energy. Despite its importance, the underlying physics of condensation initiation and propagation remain largely unknown at sub-10 nm, mainly due to the challenges of controlling and probing such small systems. Here we study the condensation of n-propane down to 8 nm confinement in a nanofluidic system, distinct from previous studies at ∼100 nm. The condensation initiates significantly earlier in the 8 nm channels, and it initiates from the entrance, in contrast to channels just 10 times larger. The condensate propagation is observed to be governed by two liquid-vapor interfaces with an interplay between film and bridging effects. We model the experimental results using classical theories and find good agreement, demonstrating that this 8 nm nonpolar fluid system can be treated as a continuum from a thermodynamic perspective, despite having only 10-20 molecular layers.

Phase change at the nanoscale is at the heart of many biological and geological phenomena. The recent emergence and global implications of unconventional oil and gas production from nanoporous shale further necessitate a higher understanding of phase behavior at these scales. Here, we directly observe condensation and condensate growth of a light hydrocarbon (propane) in discrete sub-100 nm (∼70 nm) channels. Two different condensation mechanisms at this nanoscale are distinguished, continuous growth and discontinuous growth due to liquid bridging ahead of the meniscus, both leading to similar net growth rates. The growth rates agree well with those predicted by a suitably defined thermofluid resistance model. In contrast to phase change at larger scales (∼220 and ∼1000 nm cases), the rate of liquid condensate growth in channels of sub-100 nm size is found to be limited mainly by vapor flow resistance (∼70% of the total resistance here), with interface resistance making up the difference. The condensation-induced vapor flow is in the transitional flow regime (Knudsen flow accounting for up to 13% of total resistance here). Collectively, these results demonstrate that with confinement at sub-100 nm scales, such as is commonly found in porous shale and other applications, condensation conditions deviate from the microscale and larger bulk conditions chiefly due to vapor flow and interface resistances.