Metastable equilibrium contact angle

Fig. 1. Capillary forces at the edge of a macroscopic drop, (metastable) equilibrium contact angle.

Figure 3.7 Stable bulge-like (a) and metastable ridge-like (b) drop morphology on a chemical channel with sharp chemical steps. The equilibrium contact angle on the channel and the reduced fluid volume are 6 eq = 38° and V= 4.0, respectively. The channel edges, at which the contact line is pinned, are indicated by red lines, and the free three-phase contact line on the channel is indicated by the black line. The figure is provided from Ref. [116] (Fig. 4.3) by courtesy of the author.

In the metastable configuration, the reaction product layer does not extend beyond the edge of the drop (Figure 2.24.b). As a consequence, the final contact angle 0F, calculated by considering the effect of a small displacement of the triple line around the equilibrium position, is ... 

Whatever the composition of the Ni-Si alloy, the adsorption of Ni, r, at the alloy/SiC interface is positive, corresponding to YNi/XNi values of 1.5 to 2. Enrichment of the interface in Ni indicates that interactions between Ni and SiC at the interface are stronger than those between Si and SiC. The work of adhesion of pure Ni on SiC in metastable equilibrium (i.e., for a supposed non-reactive Ni/SiC system), evaluated in Appendix I, is W 1 = 3.17 J/m2. This value is reported in Figure 7.6 along with the corresponding values of work of immersion and contact angle. 

In this equation, Qm is the molar surface area, m i is a structural parameter defined in Section 1.1 (see Figure 1.3) and A is the regular solution parameter of Ni-Si alloy defined by equation (4.3). From the slope of the osL(XNi) curve for XNi— 0, the adsorption energy is found to be E i,(f ) = —8.2 kJ/mole. Thus, in equations (1.2), all the quantities are known (or can be easily estimated), except W and Wf 1 which represent respectively the work of adhesion and the work of immersion of pure liquid Ni in metastable equilibrium with SiC (i.e., for a supposed non-reactive pure Ni/SiC system). The values deduced from equation (1.2) are Wj4 = 3.17 J/m2 and W = —1.35 J/m2 for pure Ni. They are reported in Figure 7.6 along with the corresponding value of contact angle. 

N.B. The above descriptions assume thermodynamic equilibrium to be attainable. In practice, it is common to observe the phenomenon of wetting hysteresis. Metastable rather than stable equilibrium is reached, as shown experimentally by a range of contact angles instead of a unique value. The causes are multiple heterogeneity of the solid surface, local adsorption. Roughness of surfaces, and so on. 

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