surfaces due to their durable non-wettability for deposited and impacting droplets [37-42, 98]. However, many recent studies reported that the superhydrophobic surfaces lose the non-wetting characteristics during condensation [13, 14, 16, 17]. Such phenomenon may partly be attributed to the degradation of surface structures and coatings, but the random water nucleation behavior is still the major reason for the loss of superhydrophobicity on surfaces.
Based on classical nucleation theory, the critical radius of water embryos is approximately several nanometers at atmospheric pressure. Although we showed the concave geometry favors the nucleus formation (Section 2.2.1), the water nucleation process is virtually independent of the microscale surface morphology since almost all surface textures have local concave structures at the nanoscale, either due to edges or surface roughness. Experimental images obtained via environmental scanning electron microscopy (ESEM) have demonstrated that the water embryos can randomly nucleate on bottom as well as on top of the surface structures of superhydrophobic coatings with homogeneous surface chemistry (see Figure 2.5) [18, 60, 62]. The different nucleating locations of water embryos determine the final wetting state of condensed droplets on the surface. Miljkovic, Enright and coworkers [19, 61, 86] showed that the initial water nucleation within the nanostructures results in a partial-wetting (PW) droplet morphology, as shown in Figure 2.6b. Compared with the droplet fully suspended on top of surface structures in Cassie-Baxter state (Figure 2.6a), the PW droplet has a relative higher droplet-surface adhesion as it locally wets the surface between nanostructures (i.e., with water-filled nanostructures under a portion of the Cassie droplet). More importantly, at higher supersaturations, the random nucleation process also induces a “condensate flooding” on the superhydrophobic surfaces, which manifests as the loss of surface superhydrophobicity during condensation. Owing to the decreasing nucleation distance LN of water embryos, nano-droplets can coalesce within the nanostructures and form a pinned liquid film instead of PW droplets. Further condensation on such “flooded” area consequently leads to the formation of immersed Wenzel-state droplets which exhibit significant adhesion on condensing surface, as shown in Figure 2.6c. This surface flooding dramatically decreases the overall condensation rate because these immobile Wenzel droplets act as a thermal barrier to hinder the heat and mass transfer of phase transition [43, 44].
Figure 2.5 (a1-a3) ESEM images showing the random water nucleation on a superhydrophobic surface consisting of an array of hydrophobic square posts with width, spacing, and height of 15µm, 45µm, and 105µm, respectively. (b1-b3) ESEM snapshots showing the random water nucleation on a superhydrophobic surface consisting of nanowires with diameter, spacing, height of ~400nm, ~700nm, and ~2.6µm, respectively. The nano-droplets can nucleate either on top (b1) or on bottom (b2) of nanostructures. Due to the different nucleating location of water embryos, the condensed water will grow to microscale droplets in Cassie and Wenzel-states. (The intrinsic contact angle of the hydrophobic coating for both (a) microstructured and (b) nanostructured surfaces is ~110°). Part (a) is reprinted with permission from [62]. Part (b) is reprinted with permission from [18].
Figure 2.6 ESEM snapshots showing the condensed droplets in (a) Cassie-Baxter, (b) partial-wetting, and (c) Wenzel morphologies on the superhydrophobic nanostructures. Parts a and b are reprinted with permission from [86].
In fact, the heterogeneous nucleation rate is also governed by the intrinsic contact angle on surface, which solely depends on the liquid and surface chemistry. In simple terms, hydrophilic surfaces are more favorable for water nucleation than hydrophobic surfaces. Thus, the spatial control of nucleation sites can be realized by manipulating the local wettability on the condensing surface. Varanasi et al. [62] first revealed that the heterogeneous nucleation of water droplets can be spatially controlled via modification of the local intrinsic wettability of a surface (see Figure 2.7a). In contrast to the random nucleation behavior, the micro-pillar arrays with hydrophilic tops promote the nucleation and growth of Cassie-type droplets on condensing surface [69]. To avoid the droplets transition to the Wenzel-state in continuous condensation [63], novel surfaces consisting of multiscale roughness and hybrid wettability were further developed with assistance of nanofabrication techniques [64, 65, 68, 70, 71]. With a proper design of mixed wettability, the hybrid surfaces can guarantee the selective water nucleation on hydrophilic areas, while promoting the coalescence-induced droplet departure due to the presence of superhydrophobic nanostructures [21, 22, 45] (see Figure 2.7b). A recent numerical study of heterogeneous water nucleation showed that the coalescence of nano-droplets on a hybrid nanopillar surface can even pull the water molecules out of the gap between nanopillars, as shown in Figure 2.7c [57]. This finding demonstrates a great potential for the hybrid surface to delay the surface flooding under condensation at higher supersaturations. Nevertheless, given the limited experimental characterizations, we should admit that the correlation of hybrid-wettability structures and water nucleation dynamics (e.g., nucleation rate and density) remains inadequately understood. The long-term control of water nucleation and condensation behaviors remains challenging, which requires more effort on the surface engineering and associated theoretical investigations.
Figure 2.7 (a) ESEM snapshots showing the selective water nucleation on the surface with hybrid wettability. The micro-posts are 3 µm in width, 4.5 µm in spacing, and 9 µm in height. The intrinsic contact angles of the hydrophilic and hydrophobic regions are ~25° and ~110°, respectively. (b) Time-lapse ESEM images showing the selective water nucleation atop the hydrophilic micropillars of surface with hybrid wettability. White dashed line represents the coalescence-induced droplet departure on biphilic surface. The intrinsic contact angles of the hydrophilic and hydrophobic regions are ~20° and ~110°, respectively. (c) MD simulation results showing the water nucleation process on hybrid nanopillar surface (pillar geometry: 18.1Å in height, 23.5Å in width and 12.5Å in interpillar spacing). The coalescence of nano-droplets gradually pulls the bottom water molecules out of the valley of pillars, forming a new droplet on top of nanopillars. Part (a) is reprinted with permission from [62]. Part (b) is reprinted with permission from [67]. Part (c) is reprinted with permission from [57].
2.2.4 Heterogeneous Ice Nucleation in Supercooled Water
Compared with the direct heterogeneous ice nucleation from vapor (i.e., desublimation), the ice nucleation in supercooled water on surfaces is more prevalent in nature. Detailed analysis about the preference for heterogeneous desublimation and supercooled condensation will be discussed in Chapter 4. Here, we focus on the most common icing phenomenon i.e. ice nucleation in a condensed droplet at temperatures below the freezing point.
