  Motived by recent ground-based and microgravity experiments investigating the
interfacial dynamics of a volatile liquid (FC-72, $Pr=12.34$) contained in a
heated cylindrical cell, we numerically study the thermocapillary-driven flow
in such an evaporating liquid layer. Particular attention is given to the
prediction of the transition of the axisymmetric flow to fully
three-dimensional patterns when the applied temperature increases. The
numerical simulations rely on an improved one-sided model of evaporation by
including heat and mass transfer through the gas phase via the heat transfer
Biot number and the evaporative Biot number. We present the axisymmetric flow
characteristics, show the variation of the transition points with these Biot
numbers, and more importantly elucidate the twofold role of the latent heat of
evaporation in the stability; evaporation not only destabilizes the flow but
also stabilizes it, depending upon the place where the evaporation-induced
thermal gradients come into play. We also show that buoyancy in the liquid
layer has a stabilizing effect, though its effect is insignificant. At high
Marangoni numbers, the numerical simulations revealed smaller-scale thermal
patterns formed on the surface of a thinner evaporating layer, in qualitative
agreement with experimental observations. The present work helps to gain a
better understanding of the role of a phase change in the thermocapillary
instability of an evaporating liquid layer.
