Line Contact

Very small sessile drops have a shape that depends on the line tension along the circular contact line if large enough it induces a dewetting transition detaching the drop from the surface [84]. 

Fig. X-7. Advancing and receding contact angles of octane on mica coated with a fluo-ropolymer FC 722 (3M) versus the duration of the solid-liquid contact. The solid lines represent the initial advancing and infinite time advancing and receding contact lines and the dashed lines are 95% confidence limits. (From Ref. 75.)...

Plot the shape of the contact line pinned to a defect using Eq. X-30 for water on polyethylene, stearic acid, and platinum. Assume that the upper cutoff length is 2 mm. How does the shape of the pinned contact line compare with your observations of raindrops on dirty windows ... 

Sillinian, W. J. and Scriven, L. E., 1980. Separating flow near a static contact line slip at a wall and shape of a free surface.. /. Comput. Phys. 34, 287-313. 

Contacts with other pipelines or grounds can be localized to within a few hundred meters by pipe current measurements. Contacts with foreign pipelines or cables can also be found by measuring potential at the fittings of the other line while the protection current of the cathodically protected pipeline is switched on and off. While the potential of unconnected pipelines will assume more positive values when the protection current is switched on, the cathodic current may also enter any line in contact with the cathodically protected pipeline and thus shift its potential to more negative values. Should the contacting line not be located by this method, fault location can be attempted with direct or alternating current. 

As indicated, an implicit assumption of the JKR theory is that there are no interactions outside the contact radius. More specifically, the energy arguments used in the development of the JKR theory do not allow specific locations of the adhesion forces to be determined except that they must be associated with the contact line where the two surfaces of the particle and substrate become joined. Adhesion-induced stresses act at the surface and not a result of action-at-a-distance interatomic forces. This results in a stress singularity at the circumference of the contact radius [41]. The validity of this assumption was first questioned by Derjaguin et al. [42], who proposed an alternative model of adhesion (commonly referred to as the DMT theory ). Needless to say, the predictions of the JKR and DMT models are vastly different, as discussed by Tabor [41]. 

Dussan EBV (1979) On the spreading of liquids on solid surfaces static and dynamic contact lines. Ann Rev Fluid Mech 11 371 00... 

Figure 8 shows H2SO4 droplets on mica at very low humidity (<5%). The contact line aronnd the drops is smooth and circnlar, revealing that no pinning has occurred [49]. Although the area between drops is flat, it does not correspond to clean mica but to a liquid film covering it of a few monolayers thickness. This is deduced from the hysteresis in the force versns distance experiments, where the tip is brought into contact with the surface and then pulled off. 

As the wetting front advances at speed U, the solid undergoes a strain cycle at a variety of frequencies, /, the local frequency depending on the distance of the element of solid from the contact line at the moment under consideration. The solid the furthest from the contact line, yet still perturbed by the presence of the three-phase line, is at a distance of ca. to and thus feels a strain cycle at frequency [//to. At the other extreme, near the lower cutoff at x = 8, the frequency is ca. [7/8. The latter frequency will be dominant, since it is in the direct vicinity of the three-phase line that the solid is strained the most. As a consequence, and using Eq. (10), we can define the rate at which work is being done as ... 

It has been shown that contact angle hysteresis might arise as a result of inhomogeneities of the surface wetted by the liquid phase or surface roughness [70]. When surface roughness plays a considerable role, the observed contact angle may depend on the exact position of the contact line with respect to the microscopic or... 

While the above refers mainly to the static limit, new effects come into play when a moving contact line, i.e. spreading, is considered. It has been observed experimentally that the contact angle of a moving contact line 0, the dynamic contact angle, deviates from the corresponding static value 0. As an example, for a completely wettable surface (i.e. 6(, = 0), a relationship of the form... 

The constraint to be implemented at the three-phase contact line between the two fluids and a solid surface requires that the contact angle 0 (compare Figure 2.58) assumes a prescribed value. As discussed in Section 2.2.3, the contact angle might also be allowed to vary with the velocity of the contact line. Especially in microfluidic... 

Figure16.6 (a) Schematicdrawingofexperimental set-upforthe evaluation of the interfacial tension under potential control, (b) Relative change in contact angle as a function ofthe potential after the substrate was inserted into (open circles) and pulled from the nitrobenzene phase. Insets are schematic drawings of the side views of the contact lines. The potential was described with respect to the Au/AuO f reference electrode.

Consider two equal spheres held together by a liquid bridge, as shown in Fig. 4. Two forces contribute to the tensile strength of the bond in an additive fashion the pull due to surface tension at solid-liquid-gas contact line directed along the liquid surface and the negative capillary pressure or the... 

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