Ice Adhesion. Группа авторов
T(t′) is regarded as a monotonically decreasing function of time i.e., T(t′) <0. The surface temperature first reaches the saturation point (T = Tsat) at t = t0, and further decreases to the subcooled condition, T < Tsat. Thus, Eq. 2.17 can be readily expressed as a function of the surface temperature T(t′),
where T(t0) = Tsat, T(t) = Ts, and C(T′) = –dT′ / dt′ represent the surface cooling rate as a function of surface temperature T. Rearranging the equation, we can obtain the critical surface area A* to form one water nucleus,
(2.19)
Because the spatial distribution of nucleation sites was in good agreement with the Poisson distribution [33], the mean nearest neighbor distance of water nuclei (LN) can be expressed as,
where N = 1/A* is the initial nucleation density of water embryos on a condensing surface. Eqs. 2.17 to 2.20 provide a fresh view on the heterogeneous nucleation process on surfaces, yet more experimental investigations are still required to provide direct evidence for validating the predictions of this models for the nucleation density on surface.
2.2.3 Spatial Control of Water Nucleation on Nanoengineered Surfaces
The ability to control nucleation is of great importance to many applications involving phase transitions, such as distillation, power generation, crystallization and anti-freezing. As indicated by the models of classical theory, the heterogeneous nucleation rate of single water embryo is dramatically affected by the intrinsic water contact angle and topography of the nucleation site (Eqs. 2.11 to 2.15). Considering the critical water nucleus radius (~10 nm) and nucleation density (~1010 m-2) for atmospheric condensation, the micro/nanoscale surface features can have an important influence on not only the single droplet nucleation process but also on the global condensation dynamics.
The recent development of functional surfaces and experimental techniques has led to exciting improvements in manipulating nucleation behaviors, and better understanding of the underlying physics. In the past decade, much attention has been paid to the super-liquid-repellent 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