Fundamental Limits of the Spatial Control of Heterogeneous Nucleation on Biphilic Surfaces

Condensation of water vapor on nonwetting surfaces, termed dropwise condensation, leads to rapid droplet removal and significantly improves heat transfer compared to wetting surfaces. However, the spatial distribution of heterogeneous nucleation sites during dropwise condensation is random. Furthermore, the low surface energy of the nonwetting substrate reduces the nucleation rate as predicted by classical nucleation theory. To achieve higher nucleation rates, biphilic surfaces having low nucleation energy barriers that rely on spatial heterogeneity of surface chemistry have been developed. Here, we use a robust method to create biphilic surfaces on flat and micropillar samples having various dimensions (pillar lengths: 10-15 μm, pillar heights: 0-15 μm) by utilizing lift-off microfabrication. Our fabrication approach leads to hydrophilic pillar tops and hydrophobic pillar sides and surrounding basal areas. To study water vapor condensation on the biphilic surfaces, we utilized optical microscopy in a controlled temperature and humidity environment. Interestingly, our studies show that while the majority of nucleation (≈100%) occurred only on the hydrophilic areas (pillar tops) for small pillar center-to-center spacing (pitch), the spatial control of heterogeneous nucleation broke down when the pitch increased. For larger pitches, we observed the nucleation of water droplets on the hydrophobic base in conjunction with hydrophilic pillar tops. Using theoretical models of vapor diffusion coupled with heat transfer and three-dimensional (3D) numerical simulations, we show that nucleation initiation on hydrophilic pillar tops leads to the formation of dry zones, preventing nucleation on hydrophobic regions. However, with increasing pitch, part of the hydrophobic region no longer feels the presence of the vapor depletion zone, resulting in subsequent nucleation at defect sites on the hydrophobic regions at the base. Our study offers insights into the fundamental limitations of biphilic condensation and offers avenues for their further improvement for applications such as boiling, icing, evaporation, and condensation.