Role of molecular phonons and interfacial-temperature discontinuities in water evaporation

During steady-state water evaporation, when the vapor phase is heated electrically, the temperature on the vapor side of the interface has been reported to be as much as $27.83°\mathrm{C}$ greater than that on the liquid side. The reported interfacial temperatures were measured with thermocouple beads that were less than $50\mu \mathrm{m}$ in diameter and centered $35\mu \mathrm{m}$ from the interface in each phase. We examine the reliability of these measurements by using them with a theory of kinetics to predict the interfacial-liquid temperature. The predicted temperature discontinuities are found to be in agreement with those measured up to a temperature discontinuity of $15.69°\mathrm{C}$, but larger discontinuities cannot be confirmed because of uncertainties in the vapor-phase pressure measurements. The theory of kinetics used in the analysis includes molecular phonons in the expression for the evaporation flux. We show it is essential to include these terms if the theory is to be used to predict the temperature discontinuities.

Figure 1

(Color online) Temperatures measured as a function of depth in the liquid and vapor phases during steady-state evaporation when the liquid was held in a PMMA funnel (EA1, ), in a stainless-steel (EO7, Table ) or in a PVC funnel (EH45, Table ). Note the different magnitudes of the interfacial temperature discontinuities.

Figure 2

Schematic of the polyvinylchloride funnel with a rectangular mouth opening [1, 2]. This funnel was enclosed in a chamber that allowed the thermocouple to be monitored from outside. The constantan-heating-element temperature could be set as high as $80°\mathrm{C}$ during steady-state water evaporation. See Table . In a second set of experiments, a platinum-mica heating element that could be set up to a temperature of $200°\mathrm{C}$ replaced the constantan-heating-element. See Table .

Figure 3

(Color online) The iteration procedure used to calculate the temperature discontinuity for experiment EA8, Table is illustrated.

Figure 4

(Color online) The calculated value of the interfacial temperature discontinuity compared with that measured when water evaporated at the circular mouth of a PMMA funnel. The error bars reflect the uncertainty in the vapor-phase pressure measurements.

Figure 5

(Color online) The calculated value of the interfacial temperature discontinuity compared with that measured when water evaporated at the rectangular mouth of a stainless-steel funnel. The error bars reflect the uncertainty in the vapor-phase pressure measurements.

Figure 6

(Color) The calculated value of the interfacial temperature discontinuity compared with that measured when water evaporated at the rectangular mouth of a PVC funnel. In some of the experiments the vapor phase was heated up to a maximum of $80°\mathrm{C}$ (Table ) at a position approximately $4\mathrm{mm}$ above the liquid-vapor interface. The error bars reflect the uncertainty in the vapor-phase pressure measurements.

Figure 7

(Color) The calculated value of the interfacial temperature discontinuity compared with that measured when water evaporated at the rectangular mouth of a PVC funnel. The five experiments for which there is disagreement between the predicted and measured interfacial temperature discontinuities are indicated as those for which the heating element was at a temperature of $100°\mathrm{C}$ or more. The error bars are shown with the symbol for each experiment, but are not always visible.