Contact lines adhesion

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]. 

Also adhesion between the tip and sample can cause deformation of the sample. Several theories have been developed to include the effect of adhesive forces. In the JKR theory adhesion forces outside the contact area are neglected and elastic stresses at the contact line are infinite [80]. Even under zero load, the adhesion force results in a finite contact radius a=(9jtR2y/2 E)1/3 as obtained from Eq. 7 for F=0. For example, for a tip radius R=10 nm, E=lGPa, typical surface energy for polymers y=25 mN/m, and typical SFM load F=1 nN, the contact radius will be about a=9.5 nm and 8=9 nm, while under zero load the contact radius and the deformation become a=4.5 nm and 8=2 nm, respectively. The experiment shows that under zero load the contact radius for a 10 nm tungsten tip and an organic film in air is 2.4 nm [240]. The contact radius caused only by adhesion is almost five times larger than the Hertzian diameter calculated above. It means, that even at very small forces the surface deformation as well as the lateral resolution is determined by adhesion between the tip and sample. 

In adhesion measurements one is confronted with some of the problems of cleavage experiments. Deformation occurs close to the contact line, although in this case deformation is. to a large extent, clastic. In addition, the range of surface forces needs to be considered. 

Figure 26.11]. This is a result of the strong adhesive forces due to the strong interactions of the high-energy surface and water molecules. The three-phase contact line starts to advance toward the dry surface (b c) immediately after contact is made with the water. In this case, the two-stage line (A C) in Figure 26.9 appears as a straight line as in the force loops of (TMS-I-02)-treated polymers depicted in Figure 26.12.

Figure 26.10, and (d e) in Figure 26.11] until the force in the direction of the wet surface exceeds the adhesive tension of emersion, Te, at the polymer surface/water interface. After exceeding the adhesive tension, the three-phase contact line starts to move toward the prewetted surface, seen as (D E) in Figure 26.9 and (C D) in Figure 26.12. The adhesive tension in the receding process is usually less than that in the advancing process unless the surface was completely wetted by the first immersion (i.e., zero contact angle). When the complete wetting occurs on the first immersion, the first emersion line retraces the first immersion line, such is the case with O2 plasma-cleaned glass.

An adhesion force component A y caused by the boundary force at the solid-liquid-gaseous contact line, which is determined by the surface tension of the liquid ot ... 

The free energy or tension of adhesion, r, for a solid-liquid system is defined as the difference between the interfacial free energies or tensions at the S/A and S/L interfaces on the contact line R between these two interfaces and the L/A interface. The variation of the adhesion tension with composition of the liquid phase therefore must follow the variations of the corresponding adsorption equilibria (and tensions) at the corresponding interfaces. 

For very small dynamic contact angles, the liquid is not completely removed by the split streamline and it is entrained between the film and the solid surface, creating what is known as a wet LB film. Water trapped between the solid surface and the LB monolayer prevents adhesion and is a leading cause of monolayer instability. Petrov etal. (1980) sketched the flow pattern near the moving contact line. The flow pattern is the one described here for region IV. The authors, however, reference Huh and Scriven (1971)... 

Desemo M, Muller MM, Guven J (2007) Contact lines for fluid surface adhesion. Phys Rev E 76 011605. doi 10.1103/PhysRevE.76.011605... 

Among the above parameters, the following require computation of the membrane deformation (1) the location of the contact line w.r.t the particle (represented by the distances a fe), (2) the traction along the liquid-gas interface and (3) the internal pressure p. Friction and surface adhesion between the particle and the substrate are not considered in this work. The example shown in Figure 5.4 represents a special case of the general model depicted in Figure 5.2 where the contaminant particle can be initially located anywhere on the droplet surface. 

Callegari G, Calvo A, Hulin J. (2006) Contact line motion Hydrodynamical or molecular process In KL Mittal (ed), Contact Angle, Wettability and Adhesion, Vol. 4. VSP, Leiden. 

Fluid/liquid/solid adhesion has a predominant roie in a great number of natural and industrial processes, and it is widely investigated. Displacement of the three-phase contact line usually takes place in both the formation and the ceasing, and the modification of the adhesion. The essential problem is how the contact line can move and what the mechnism of the displacement is. 

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