Macroscopic contact angle

The question has been taken up again recently by L. R. White who distinguishes between the macroscopic and the microscopic contact angles (Fig. 3.9). The macroscopic contact angle 6 is governed by the slope of a... 

Fig. 3.9 Macroscopic contact angle 0, and microscopic contact angle 0,. S = solid L — liquid G = gas. (White .)...

Figure 6 shows droplets of KOH solution on mica produced by similar methods. In both cases the drop profiles are very close to a spherical cap. In Figure 7 we have plotted the effective contact angle as a function of droplet height. The deviation from the macroscopic contact angle with decreasing droplet volume can clearly be seen. 

Figure 1.7. Dependence of contact angle on the metal droplet radius for Pb on vitreous carbon at a temperature close to the melting point of Pb. The horizontal line identifies the macroscopic contact angle. Data from work reported in (Chizhik et al. 1985).

Figure 1.18. Model sawtooth surface used in calculations of the free energy of a meniscus. 0M represents the macroscopic contact angle at each height z of the triple line.

Figure 1.20. Reduced free energy per unit length of triple line of a meniscus on the solid surface shown in Figures 1.18 and 1.19 plotted as a function of the macroscopic contact angle. The physical parameters used in the calculation are p = 7 x 103kg.m 3,<7LV = 1 J.m 2,0Y = 40°, g = 9.81 m.s 2, fi = 10° and Lf = 100 /im. Results from (Eustathopoulos and Chatain 1990) [1],...

Therefore, by extrapolating the meniscus profile (in the meniscus, far from the film, the condition (3.39) holds) to its intersection with the extrapolated film surface at z = z = hi2, the macroscopic contact angle 6h is defined and... 

In this section we shall discuss the measurement of macroscopic contact angles under conditions that are as close as possible to equilibrium. These contact angles are not necessarily identical to those on a molecular scale and certainly not to contact angles with a precursor film. In other words, we are essentially discussing macroscopic mecisuring techniques. 

Eor the Plateau border we have z > / , 11 -> 0, o -> o = const., and both Equations 5.150 and 5.151 rednce to Eqnation 5.101 with AP = P. The macroscopic contact angle, a, is defined as the angle at which the extrapolated meniscns, obeying Equation 5.101, meets the extrapolated film snrface (see the dashed line in Fignre 5.16). The real surface, shown by solid line in Figure 5.16, differs from this extrapolated (idealized) profile, because of the interactions between the two film snrfaces, which is taken into acconnt in Eqnation 5.150, but not in Eqnation 5.101. To compensate for the difference between the real and idealized system, the line and transversal tensions are ascribed to the contact line in the macroscopic approach. In particnlar, the line tension makes up for the differences in snrface tension and running slope angle ... 

Churaev et al. (1994) recently published actual results on the relationship between wetting film thickness h and disjoining pressure 11, from which the macroscopic contact angle of the liquid on the substrate can be calculated. Today a compact monolayer is known as a French pancake, a bilayer a Swedish pancake and thick films as an American pancake. To sum up, wetting films and their transitions are combined with dynamic processes which elucidate rather complex and yet unsolved issues. 

Figure 7.33. Side-view of a partially wetting drop on a solid surface showing the macroscopic contact angle and the three interfacial tension vectors acting on the three-phase contact line (tcl)...

The cleaning procedure of PTFE and PE wafers was as follows the surfaces were rinsed with alcohol and water, then the substrates were soaked in a sulfochromic acid from 30 to 60 minutes at the temperature 50°C. The surfaces then were washed with distilled water and dried with a strong jet of nitrogen. The equilibrium macroscopic contact angles obtained were 105° and 90° for PTFE and PE substrates, respectively (for pure water droplets). 

Electrowetting concerns the use of an externally applied electric field to actuate or manipulate small volumes of liquid by altering its interfacial tension and hence the macroscopic contact angle or by inducing bulk liquid motion through an interfacial electric stress. 

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