Surface force three-phase contact line

At the three-phase contact line the surface tension exerts strong forces on the surface. For instance, if we consider a water drop on a polymer surface, typical contact angles are 90°. The surface tension pulls upwards on the solid surface. If we estimate the wetting line to have a width of 6 = 10 nm, the force F per unit length l can be related to the effective pressure exerted on the solid surface ... 

The equation results from the following consideration. At equilibrium the three-phase contact line does not move. Hence, the sum of the forces acting in horizontal direction must be zero. The surface of liquid A pulls with a force (per unit length) of 7a cos 03 to the left. The surface of liquid B pulls to the right with a force 7b cos i and so does the liquid A-liquid B interface 7ab cos 2. 

In the classical treatment of the interfacial tension, the force balance at the three-phase contact line (liquid-surface-air) is considered, and the interfacial tension, 7sl, is given by the surface tension of the solid, 7s, and the surface tension of the liquid, Yl, as... 

Similar to (TMS -f O2) plasma-treated PP, many of the (TMS -f O2) plasma-treated polymers showed that the three-phase contact line hardly recedes on the wet surface. Specifically, (TMS + O2) plasma-treated PTFE, UHMWPE, PP, HDPE, PVDF, and nylon showed hardly any change in contact area during the receding process. This is due to the strong specific attractive forces formed at the surface underneath the bulk droplet, i.e., the interfacial tension (underneath the droplet) changed due to the interaction of water with the surface. 

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.

When liquid molecules are adsorbed onto a solid surface, their surface concentration will be a function of the distance along the solid, and of time, in a band close to the three-phase contact line. Consequently, there will also be a corresponding gradient of surface free energy density, which will directly affect the horizontal component of force at the three-phase line resulting in contact angle hysteresis. 

The interfacial behavior of block copolymers is of interest in several fields like stabilization of emulsions, foams, and wetting control [154]. Gerdes et al. [155] studied the wetting behavior of aqueous solutions of triblock copolymers on silica. The experimental approach was based on the use of a Wilhelmy force balance and direct images of contact angle. Their results show that the three-phase contact line advances in jumps over the surface when it is immersed at constant speed into the copolymer solution. Apparently the stick-slip spreading mechanism is the same as has been proposed for short chain cationic surfactants. 

The surface phenomena are determined by the forces acting in thin liquid films or layers in the vicinity of the apparent three-phase contact line [1]. 

The range of action of surface forces is usually of the order of 0.1 pm [1]. Note that in the vicinity of the three-phase contact line (Fig. 1), the liquid profile tends to zero thickness. The latter means that close to the three-phase contact line surface forces come into play and their influence cannot be ignored. 

A manifestation of surface forces (either between particles, bubbles, and emulsion droplets or in the vicinity of the three-phase contact line (Fig. 1)) is the disjoining pressure. Let us consider the interaction of two thick plain parallel surfaces divided by a thin layer of liquid of thickness h (e.g., aqueous electrolyte solution) in Fig. 2. The surfaces are not necessarily the same, as shown by two examples (i) 1 is air, 3 is a liquid film, and 2 is solid support (ii) 1 and 2 are air or a liquid, and 3 is a liquid film (of a different liquid). Example (i) is as a liquid film on a solid support and models a liquid layer in the... 

Such boundary layers exist in proximity to any interface solid-liquid, liquid-liquid, and liquid-air. In the vicinity of the apparent three-phase contact line (Fig. 3), those boundary layers overlap. The overlapping of boundary layers is the physical phenomenon which results in the existence of surface forces. Let the thickness of the boundary layers be 8. In the vicinity of the three-phase contact line, the thickness of a droplet/ meniscus, h, is small enough, that is, /i 8, and, hence, boundary layers overlap (Fig. 3), which results in the creation of disjoining pressure. A similar situation occurs at a contact of two particles in a liquid (Fig. 4). The abovementioned characteristic scale of boimdary layer thickness, 8 10 cm, determines the characteristic thickness where the disjoining pressure acts. 

The liquid surface near the three-phase contact line is oriented almost vertically. Thus, the surface tension drags the plate downward. For a rectangular plate of dimensions I, w, and t, immersed to a depth in a liquid (as shown in Fig. 3), the net downward force, F, is given by... 

Before we start a discussion on the thermodynamics of a contact between particles, it is worthwhile to briefly address the phenomena taking place at the three-phase contact line, and in particular, wetting and capillary forces acting within a liquid meniscus. We will also briefly summarize the principal methods of surface tension measurement. 

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