We should consider all complex interrelated processes of heat and mass transfer including convection, conduction and radiant heat transfer in droplets as well as in the surface vapor–gas layer. Investigate high-temperature heating and evaporation of water droplets by taking into account the basic interrelated processes of heat transfer and phase transitions. Typical velocity and temperature profiles may be found in the high-temperature gas–water droplet system with varied external gas medium temperature.
I do not have direct answer to your question but ones tried to estimate evaporation time for the drop through the simple model of evaporation and oscillation movement of the drop over the hot surface due to vapour flow.
Measure the evaporation rate with the microscope. In the attached material I present a little more detail to this technique. Use different media to deposit a drop of distilled water of known amount. For an experimental series the support must have approximately the same water-solid interfacial tension. Close the space in the eyepiece and the microscope holder with a volume plexiglass box calculated that the complete evaporation of the drop of 0.2 gr, for example, does not change by more than 1% the partial pressure of the water vapor. You should see a drop of water deposited on the support very well the equivalent in the eyepiece of about 10-15 mm. Measure the time until the water disk disappears from the support. Modify the surface of the substrate by adding granules from the same material. The support and the granules to be added must not absorb the water. With these determinations you can check the validity of mathematical models or calculation programs.