Thermocapillary transport of energy during water evaporation

Abstract

When evaporation occurs at a spherical water-vapor interface maintained at the circular mouth of a small funnel, studies of the energy transport have indicated that thermal conduction alone does not provide enough energy to evaporate the liquid at the observed rate. If the Gibbs model of the interface is adopted and the "surface-thermal capacity" is assigned a value of 30.6+/-0.8 kJ/(m2 K), then for evaporation experiments with the interfacial temperature in the range -10 degrees C< or =TLV< or =3.5 degrees C and Marangoni number (Ma) in the range 100<Ma<22,000, it was found that if energy transport by both thermocapillary convection and thermal conduction were taken into account, conservation of energy was fully satisfied. The question addressed herein is whether the assigned value of the surface-thermal capacity is an ad hoc empirical parameter or a property of the water-vapor interface that can be used in other circumstances. Accordingly, a series of experiments has been conducted in which water evaporated at cylindrical interfaces that were, on average, 4.4 times larger in area than that of the spherical interfaces used to measure the surface-thermal capacity initially. It is shown that using the value of the surface-thermal capacity determined at a spherical interface, the energy transported by thermocapillary convection and thermal conduction at a cylindrical interface is sufficient to evaporate the liquid at the observed rate. Knowing the value of the surface-thermal capacity also allows the local evaporation flux to be calculated from the measured temperature profiles in the liquid and vapor phases. The calculated local evaporation flux can then be used with statistical rate theory to calculate the vapor-phase pressure along the interface. The predicted mean vapor-phase pressure is in close agreement with that measured, and the predicted pressure gradient is consistent with that expected when thermocapillary convection is present.