A theoretical heat
and mass transfer model of volatile liquid lens
evaporation on the surface of an immiscible liquid substrate is established
in toroidal coordinates. According to the coupled boundary conditions
of heat and mass transfer at the lens surface as well as the interfacial
cooling effect, the analytical solutions of the temperature field
inside the lens and the vapor concentration field around the lens
are derived for the first time. Compared with the isothermal model,
the change of contact radius calculated by the present model agrees
well with the experimental data, especially when the liquid substrate
reaches a relatively high temperature. It also reveals that the temperature
distribution inside the lens is not uniform, which is similar to the
sessile droplet evaporation on a solid substrate surface. In addition,
the excess temperature, heat flux, and evaporation flux of the lens–air
interface increase monotonically from the lens center to the contact
line. Finally, the influences of density ratio and evaporative cooling
number
E
0
on lens mass evaporation rate
are analyzed, which shows that the lens mass evaporation rate decreases
with increasing density ratio and evaporative cooling number.