Drops on a solid surface

Fig. 2.2. Contact angle, 0. and surface energies, Vlv> 7sl nd ysv, for a liquid drop on a solid surface.

In our daily environment, the surface of a material will repel water to some degree. The degree of water repellency of a substance can be expressed in terms of the contact angle of a water drop with the surface (Fig. 7.5). According to Young s equation, the contact angle of a liquid drop on a solid surface results from... 

Young s equation is also valid if we replace the gas by a second, immiscible liquid. The derivation would be the same, we only have to replace 7l and 7sl by the appropriate interfacial tensions. For example, we could determine the contact angle of a water drop on a solid surface under oil. Instead of having a gas saturated with the vapor, we require to have a second liquid saturated with dissolved molecules of the first liquid. 

Several experimental arrangements are used to measure and analyze the wetting of liquids on solid surfaces. Typical geometries are a spreading drop on a solid surface, liquid-fluid displacement through a capillary tube, steady immersion or withdrawal of fibers, plates or tapes from a pool of liquid, and the rotation of a horizontal cylinder in a liquid (Fig. 7.12). 

Another theory of the linear energy of the contact line wetting film/bulk liquid drop on a solid surface has been developed by Churaev at al. [478]. These authors also considered both cases of negative and positive line tension. In their interpretation the transition region film/bulk can be presented [478] schematically as shown in Fig. 3.103. The dashed line 1 represents the idealised surface. The real surface is shown for two different cases in case 2 the... 

Surface tensions of low-energy surfaces like many polymers are often determined from contact angle measurements. A review of the method and its application to polymer science was written by Koberstein [ 107], In equilibrium, the contact angle of a liquid drop on a solid surface is given by the Young equation ... 

FIGURE 13.10 Drops on a solid surface showing wetting, nonwetting, and a teal equilibrium (inset)... 

Figure 2 Contact angle of a liquid drop on a solid surface.

Figure 4.7. Variation of Eq — E )/Eq with 6 for a drop on a solid surface...

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)...

This equation describes quite accurately the situation of an adhesive drop on a solid surface. The surface energies do not alter profoundly as the liquid solidifies, although stresses may build up due to shrinkage. Hence, the equation is also valid for the situation of a solid adhesive on a substrate. It follows that the adhesion maximum is obtained when cos0 = 0, that is when the liquid spreads completely. This implies the existence of larger forces between the liquid molecules and the solid, compared to that between the liquid molecules themselves, which further implies a high tt v value. The adhesive force will tend to zero for contact angles above 90°, in which case is small. 

Ford ML, Nadim A (1994) Thermocapillary migration of an attached drop on a solid surface. Phys Fluid 6 3183-3185... 

Young s equation, which describes the force balance of a liquid drop on a solid surface, is used with the usual symbols,... 

FIGURE 6.9,. Spreading of a drop on a solid surface in total wetting regime. With the naked eye, an observer can see the drop, but not the precursor film. 

Frenkel YI. (1948) On the behavior ofliquid drops on a solid surface. 1. The sliding of drops on an inclined su.iia.cc. JExp Theoret Phys (USSR) 18 659. 

Equation (3.105) gives the critical relationship of m/w for the movement of liquid drops on a solid surface. As the surface is sprayed, the adhering drops grow in size until the critical value of m/o) is reached. During this period the droplets remain spherical. 

It is clear that the adhesive and substrate must come into contact for the possibility of the formation of an adhesive bond to exist. By far, the most common situation is one where a liquid adhesive comes into contact with a solid substrate. (That obviously means close contact on a molecular scale.) Factors that affect the extent of wetting and spreading of a liquid drop on a solid surface are, therefore, of primary importance in any consideration of theories of adhesion. It is appropriate, then, that two other chapters in this handbook are devoted to these considerations. 

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