Wenzel model based investigation of heterogeneous nucleation on a coarse substrate

Heterogeneous nucleation is an important phenomenon in solidification processes. A smooth interface between the nucleus and its substrate is assumed for considerations on heterogeneous nucleation in classical nucleation theory, but this condition cannot always be satisfied for the factual heterogeneous nucleation process. The formation of a nucleus on a coarse substrate is investigated, and the effect of the roughness factor of the substrate on the nucleation barrier is discussed based on Wenzel's wetting model. It is shown that the heterogeneous nucleation barrier is generally less than that of the homogeneous nucleation barrier, and a lower intrinsic wetting angle between the nucleus and the substrate leads to easier nucleation. However, it is also found that, when the intrinsic wetting angle is less than 90 degrees, higher roughness leads to easier heterogeneous nucleation; for a certain roughness factor, an intrinsic critical wetting angle exists which decreases the heterogeneous nucleation barrier to 0. On the other hand, when the intrinsic wetting angle is larger than 90 degrees, higher roughness leads to a larger heterogeneous nucleation barrier; for a certain roughness factor, an intrinsic critical non-wetting angle exists which increases the heterogeneous nucleation barrier to the value of the homogeneous nucleation. It thus leads to the ineffectiveness of the foreign substrate for nucleation.