Heterogeneous critical nucleation on a completely-wettable substrate

Heterogeneous nucleation of a new bulk phase on a flat substrate can be associated with the surface phase transition called wetting transition. When this bulk heterogeneous nucleation occurs on a completely-wettable flat substrate with a zero contact angle, the classical nucleation theory predicts that the free energy barrier of nucleation vanishes. In fact, there always exist a critical nucleus and a free energy barrier as the first-order pre-wetting transition will occur even when the contact angle is zero. Furthermore, the critical nucleus changes its 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. Recently, Sear [J.Chem.Phys {\bf 129}, 164510 (2008)] has shown by a direct numerical calculation of nucleation rate that the nucleus does not notice this change when it crosses the coexistence. In our work the morphology and the work of formation of critical nucleus on a completely-wettable substrate are re-examined across the coexistence using the interface-displacement model. Indeed, the morphology and the work of formation changes continuously at the coexistence. Our results support the prediction of Sear and will rekindle the interest on heterogeneous nucleation on a completely-wettable substrate.