Surface excess properties from energy transport measurements during water evaporation.

When water evaporates at high rates, recent studies indicate thermal conduction to the interface does not provide enough energy to evaporate water at the observed rate and that it is perhaps thermocapillary convection that transports the remaining energy. This possibility is examined by applying the Gibbs dividing-surface approximation to develop an expression for the energy transported along the interface. When this energy transport rate is compared with that required to evaporate the liquid at the observed rate, it is found that a Gibbs excess property, the "surface-thermal capacity," can be evaluated. A series of 19 evaporation experiments has been conducted under conditions for which there was no buoyancy-driven convection and for which the evaporation rate was progressively increased. For Marangoni numbers, (Ma) less than approximately 100, the interface was quiescent and thermal conduction (the Stefan condition) correctly predicted the energy transport rate to the surface. For experiments with 100<Ma<22,000, thermocapillary convection was present and the thermal conduction did not fully account for the energy transport. However, if the surface-thermal capacity is assigned a value of 30.6+/-0.8 kJ/(m2K), then energy transport by thermocapillary convection and conduction provides the energy transport required to evaporate the liquid at the observed rate. For experiments with Ma>22,000, the interfacial flow was turbulent and viscous dissipation became important.