  It is widely believed that heterogeneous nucleation occurs without an
activation process when the surface is completely wettable. In this report, we
review our previous work [J.Chem.Phys {\bf 134}, 234709 (2011)] to show that
the critical nucleus (droplet) can exist and the activation process may be
observable. In fact, a critical nucleus and a free energy barrier always exist
if the surface potential or the disjoining pressure allows for the first-order
pre-wetting transition on a completely wettable substrate where the contact
angle is zero. Furthermore, the critical nucleus changes character from the
critical nucleus of surface phase transition below bulk coexistence
(undersaturation) to the critical nucleus of bulk heterogeneous nucleation
above the coexistence (oversaturation) when it crosses the coexistence. In this
paper the morphology and work of formation of a critical nucleus on a
completely-wettable substrate are re-examined to point out the possibility of
observing a critical droplet on a completely wettable substrate.
