Ice Adhesion. Группа авторов
2.9 (a) Free energy barriers for nucleation in a system of hard spheres with a smooth spherical seed. The seed has radii Rs = 5σ, 6σ and 7σ. The dashed curve represents the homogeneous nucleation barrier (Rs = 0σ). (b) Snapshots showing the nucleation process on spherical seeds. The seeds have radii Rs = 5σ (top) and 7σ (bottom). Parts (a) and (b) are reprinted with permission from [83].
To date, state of the art experimental techniques still do not have the spatial and temporal resolution to investigate the nanoscopic process of ice nucleation. However, the size-dependent droplet icing phenomenon reported by Hou et al. [67] offers another simple approach to analyze the ice nucleus formation on a solid surface. As expressed in Eq. 2.18, the heterogeneous ice nucleation probability is primarily a function of water temperature T(t). For a supercooled droplet condensed on a cold surface, the temperature at the droplet base (i.e., solid-water interface) is lower than at the droplet top due to the thermal resistance associated with droplet heat conduction [23, 24, 86]. Figure 2.10a shows the thermal resistance network of a partial-Wenzel droplet on a superhydrophobic surface and a hybrid-wetting droplet on a biphilic surface with hybrid wettability. If assuming the temperature of saturated vapor and rear-side of substrate is constant, the droplet base temperature (Tb) will keep on decreasing with the growing droplet size and increasing thermal conduction resistance. As a result, the ice nucleation rate and nucleation probability of supercooled droplet will increase with the growing droplet diameter, as shown in Figure 2.10b. This implies that during supercooled condensation on a flat surface, the ice embryo preferentially nucleates at the base of large droplets instead of smaller ones. Moreover, for the supercooled condensation on a liquid-repellent rough surface, partial-wetting droplet morphology is more likely to trigger the ice nucleation as compared to the suspended droplet morphology. The capillary liquid-bridges underneath PW droplet lead to not only a larger area of solid-water interface, but also a lower interface temperature due to contact with the bottom of surface structures.
Due to the exponential increase of J(T) at lower temperature, the ice nucleation rate can be estimated as J(T) = J(T0 + ∆T) = α exp(–λ∆T) in a narrow temperature interval ∆T = T–T0 around a reference temperature T0, where α = J (T0) and
Figure 2.10 (a) Schematics of the thermal resistance networks of partial-Wenzel and hybrid-wetting droplets, indicating the resistances of the droplet curvature (Rc), water-vapor interface (Rv,w), and conduction resistances of droplet (Rd), hydrophobic coating (Rhc), liquid bridges (Rl), micropillars (Rm), nanopillars (Rn), and substrate (Rsub). The red dashed line represents the liquid-solid phase boundary of the supercooled droplet where the liquid water tends to freeze into ice. (b) Correlations of the freezing probability and droplet radius with the associated droplet base temperature for a substrate temperature Tsub = 267.75 K. Both reprinted with permission from [67].
where Tm is the melting temperature of ice (273.15K), Tb and A are the temperature and contact area of solid-water interface, respectively. Tb can be determined by the heat transfer model of a condensed droplet,
in which, Tsat – Tsub is the temperature difference between the saturated vapor and substrate (with a constant temperature), and Md, Mi, and Msub are the thermal insulances (reciprocal of heat transfer coefficient) associated with the droplet conduction, interface wetting morphology, and substrate.
For a condensed droplet, the conduction insulance Md = rθw/(4kw sin θw) depends on the droplet radius r, where kw is the thermal conductivity of water. Substituting the expression of Tb and Md into Eq. 2.22, the characteristic droplet freezing radius rf is given as,
where
2.3 Prospects
Despite significant improvements in experimental techniques over the past years, it remains challenging to characterize and control the nucleation dynamics of water and ice in an accurate manner. The recent improvements in simulation methods provide complementary approaches to study the water nucleation process in various idealized environments. It enriches our understanding of the kinetic evolution of nucleating embryos, as well as their volume and interfacial structures. However, the limited computational domain and timescale greatly restrict the application of simulations for real systems. We believe many opportunities exist for the further experimental exploration of nucleation at the very beginning stage by using higher resolution or three-dimensional viewing techniques (e.g., surface plasmons, confocal microscopy, etc.). New findings of nucleus properties and interfacial phenomena will lead to new approaches to control the nucleation process on solid surfaces, not only for water but also for other low surface tension liquids.
Figure 2.11 Critical droplet freezing radius as a function of the substrate temperature.