Ice Adhesion. Группа авторов
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.
In general, the classical nucleation theory is applicable for predicting the ice nucleation rate in a supercooled droplet [27]. However, an issue arises when seeking the value of intrinsic contact angle θi,s at ice nucleus and solid interface for calculating the ice nucleation barrier. Because of the difficulty in direct observation, θi,s has not been measurable in a macroscopic way up to now. In past few years, several experiments have indicated the presence of a thin, quasi-liquid layer on ice in contact with various surfaces [99-104]. By assuming such quasi-liquid layer existing between the ice nucleus and solid surface, Eberle et al. [47] extrapolated a modified Young’s equation to estimate the contact angle of ice embryo on quasi-liquid layer for a rough surface (see Figure 2.8),
where σi,ql, σs,ql, σs,i and σs,w denote the interfacial free energies between the ice and quasi-liquid layer, the surface and the quasi-liquid layer, the surface and ice, and the surface and liquid, respectively. d and ξ denote the thickness of quasi-liquid layer and a characteristic decay length of the interaction with bulk liquid [105].
Figure 2.8 Schematic showing the heterogeneous nucleation of an ice embryo with interfacial quasi-liquid layer in a nanoscale cavity. Figure is reprinted with permission from [47].
In principle, the effect of surface geometry on the nucleus formation (Eqs. 2.11 to 2.14) is applicable to the surface structures at all length-scales, yet particular phenomena arise at the molecular level. A recent Monte Carlo simulation showed that a convex surface can activate the surface nucleation only if the radius of curvature exceeds a minimum size [83]. Figure 2.9a shows the estimated nucleation barrier on spherical seeds with various radii. When the seed radius Rs ≤ 4σ (σ is the Lennard-Jones molecular diameter), the nuclei typically form in the bulk instead of on the seed surface. The surface nucleation starts with a spherical seed with radius Rs ≃5σ . As can be seen from Figure 2.9b, very small clusters grow on the seed surface, which tend to grow outward radially due to the large surface curvature. Before reaching the critical size, the clusters detach from the surface and move into the bulk vapor phase. In this case, the critical nucleus only forms in the bulk vapor phase, which is similar to the process of homogeneous nucleation. Although the detachment of nuclei clearly affects the nucleation process, it hardly affects the nucleation barrier (see Figure 2.9a). In comparison, larger seeds (Rs > 5σ) do lower the barrier and speed up the nucleation process.
Investigations of heterogeneous ice nucleation in nano-confinements help to broaden our horizon of nucleation behaviors [106–112]. Suzuki et al. experimentally reported that the ice nucleation mechanism could be precisely regulated by confinement within nanoporous alumina [106]. When supercooled water freezes inside a nanoporous aluminum oxide membrane with pore diameters ≤ 35 nm, the heterogeneous nucleation of hexagonal ice (Ih) is evidently suppressed. Instead, the homogeneous nucleation of cubic ice (Ic) dominates the water crystallization in the nanopores. Such transition of nucleation mechanism can be understood by comparing the critical ice nucleus radius r* with the pore diameter d. That is, only when r* < d is the associated crystalline phase stable within the nanoporous materials. Using numerical method, Koga et al. also demonstrated that water encapsulated in carbon nanotubes could form various new phases of ice which were not seen in the bulk configuration [110]. Using carbon nanotubes with diameters ranging from 1.1 ~ 1.4 nm and applied axial pressures of 50 ~ 500 MPa, confined liquid water can freeze to hexagonal and heptagonal ice nanotubes. The results suggest that the water structure modification imposed by the solid surface can play an important role in the heterogeneous ice nucleation mechanism.
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