Ice Adhesion. Группа авторов
in water penetration depth, c, with a change in temperature on copper square-pillared substrates. Adapted from [108]
1.3.3 Ice Adhesion to Real Surfaces
Section 1.3.2 discussed the important concept of the Cassie-to-Wenzel transition on non-ideal surfaces. We showed that as the temperature of the surface decreases past the dew point, the intrinsic water contact angle of the material decreases, allowing water to infiltrate the pores which had previously contained air. Naturally, for ice to form on a surface, said surface needs to be below the dew point temperature. Thus, in this section we discuss the adhesion of ice to roughened substrates through real surfaces potentially being in a hybrid Cassie-Wenzel wetting state, or fully Wenzel wetting state upon freezing. This view will help to explain why some literature offers the conclusion of reduced ice adhesion strength to superhydrophobic surfaces [115–117] while others conclude that either ice adhesion is increased on superhydrophobic materials [118, 119] or that adhesion strength increases with icing/deicing cycles [120].
First, let us consider the overall mechanism for the removal of ice from a solid surface. In order for solid ice to be removed from the substrate when a force is applied, (1) a crack must be initiated; and (2) the crack must propagate. This process is shown in Figure 1.10(a) for the Wenzel wetting surface that was already considered in Section 1.3.1. What was discussed implicitly in the section on the icing of ideal surfaces, and will be done so explicitly now, is where this crack initiation and propagation occurs. If the crack is initiated, and propagated at the ice-solid interface, then the event can be considered as purely adhesional failure [108]. This is the case for the example in Figure 1.10(a). If, on the other hand, the failure occurs within the bulk of the ice (or, indeed within the bulk of the solid substrate), the mode of failure is said to be purely cohesional failure, as shown in Figure 1.10(b). A hybrid adhesional-cohesional mode of ice-solid bond failure can also occur.
Crack propagation follows a path of least resistance [121]. Thus, the mode of failure is determined by the comparison of adhesion strength of the ice-solid bond, τIS, to the tensile strengths of the ice, τI and solid, τS. The adhesion strength of the ice-solid bond is defined as the peak force applied to dislodge the ice, Fapp, normalized over the cross-sectional area of the dislodged ice. Therefore, a necessary condition for the mode of ice failure to be purely adhesional is that τIS < τI and τIS < τS. This condition is not, however, sufficient; there is also the consideration of the path that the crack must propagate along. The examples in Figure 1.10(a) and (b) are purposely drawn with substrates which possess gently curving surface morphologies. Consider instead the example in Figure 1.10(c). Again, the liquid water wetted the surface in the Wenzel state, completely filling in any void volumes. Here the surface morphology has sharp corners and walls which are rather vertical. When the water freezes, it expands and pushes against the walls, creating a tight grip on the microstructure, known as interlocking. The sharp corners would require the propagating crack to make abrupt turns in order to follow exactly the ice-solid interface. Rather what occurs is that the crack propagates along the tops of the surface asperities, and through the ice that is frozen between adjoining features. This manner of ice dislodging is considered to be hybrid adhesional-cohesional failure.
Figure 1.10 The failure mode of the ice-solid bond is said to be: (a) adhesional failure if the crack propagates along the ice-solid interface; (b) cohesional failure if the crack propagates within the bulk of the ice or within the bulk of the solid; or (c) hybrid adhesional-cohesional failure if the crack propagates both within the bulk solid/ice and along the ice-solid interface.
When a force is applied to surface ice (or indeed any object), the resulting stress is distributed throughout the material. However, if a defect exists in the ice, then the stress cannot be transferred through this region and a localized buildup of stress occurs. Crack initiation will occur preferentially at a point on the surface where residual stress has built up [108, 122, 123]. Figure 1.10 shows the crack initiating from a single point, and propagating in a single direction. Note that this is not the case in reality. An ice-solid interface may have many points of crack initiation, where the freezing process has resulted in the formation of micro-cracks, or the entrapment of air bubbles that act as local stress concentrators [108]. It is from these points that crack(s) will propagate, potentially joining other forming cracks, and eventual failure will occur.
The origin of trapped air bubbles in the ice is rather obvious, with air that had been dissolved in the water coming out of solution with decreasing temperature. However, let us consider whence micro-cracks in the ice arrive. Although fusion must occur with the water-solid interface being at the freezing temperature of water, once solid ice has formed, the temperature can continue to decrease. This potential further cooling of two solid materials invariably involves thermal expansion [94]. If the thermal expansion coefficient of the ice (~ 5.0 × 10–5/°C [124]) differs from that of the substrate it is bonded to, microcracks will be introduced at their interface. For comparison, the thermal expansion coefficient of 316 stainless steel is ~ 1.2 × 10–5/°C [125], meaning that ice will expand approximately 5 times more than a stainless steel substrate. Further, the heat capacity of ice will invariably differ from that of the solid substrate at the interface leading to local differences in temperature and therefore differences in thermal expansion.
With all of the discussion in Section 1.3 heretofore, we are now able to assess the efficacy of superhydrophobic surfaces with regards to anti-icing, and to draw conclusions as to which alternative strategies may prove to be more effective. Consider again the ideal surface presented in Section 1.3.1 which results in the Cassie-Baxter wetting state. As we cool this system from room temperature to below the freezing point, we note that our previous assumption that the Cassie-Baxter wetting state will prevail until fusion takes place will not hold on our real surface. Rather, as shown in Figure 1.11(a), the hydrophobicity of the surface will be lost as the dew point temperature is crossed. This will result in partial or complete penetration, and thus possible Cassie-to-Wenzel transition. As the temperature is lowered further past the fusion temperature the water will freeze. The ice is now interlocked into the microstructure of the surface. Upon application of a dislodging force, failure will preferentially occur along the tops of the microstructure, as shown in Figure 1.11(b). Failure here will occur in a hybrid cohesional-adhesional mode. In fact, because superhydrophobic surfaces typically possess solid area fractions ≈ 0.1 in order to maximize the air-liquid interfacial area, the crack will mostly propagate through ice [126]. Therefore, the measured ice adhesion strength will be approximately equal to the tensile strength of ice, τI. Often superhydrophobic surfaces have been shown to possess higher ice adhesion strengths than smooth surfaces of the same material for this reason[118, 119].
Figure 1.11 (a) A real superhydrophobic surface will undergo some degree of Cassie-to-Wenzel transition as the temperature is lowered below