Three-phase contact lines

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... 

Young s equation is the basis for a quantitative description of wetting phenomena. If a drop of a liquid is placed on a solid surface there are two possibilities the liquid spreads on the surface completely (contact angle 0 = 0°) or a finite contact angle is established.1 In the second case a three-phase contact line — also called wetting line — is formed. At this line three phases are in contact the solid, the liquid, and the vapor (Fig. 7.1). Young s equation relates the contact angle to the interfacial tensions 75, 7l, and 7sl [222,223] ... 

Here, a is the radius of curvature of the three-phase contact line. For a drop with circular contact area it is the contact radius. 

Dissolved substances often adsorb at the three-phase contact line. Advancing or receding of the liquid is hindered by the deposited substances. 

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 work required to create a new three-phase contact line per unit length is called line tension. It is typically of the order of 0.1 nN. For tiny liquid drops the line tension can significantly influence the wetting behavior. 

Contact angle hysteresis can be caused by surface roughness, heterogeneity, dissolved substances, and structural changes of the solid at the three-phase contact line. 

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. 

Out of the parameters appearing in the Young equation, Eq. (1), only the surface tension of the liquid can be simply and accurately measured. However, the measured value of a/ can be used in the Young equation only under a certain condition, as discussed in the following. Gibbs was the first to note that the Young equation may need to be modified, even for an ideal solid surface. This is so because the three interfacial tensions may be influenced by each other at the three-phase contact line, due to the effect that one phase may... 

The Young equation contains the surface tension of the liquid yi - which can easily be measured, and the difference of the surface tensions of the solid-vapor ysv and the solid-liquid interface ysL That the surface tension enters the Young equation is not beyond doubt. Linford I6 inserted the generalized intensive surface parameter ys, arguing that at the three-phase contact line elastic deformations take place. In accordance with Rusanov [I7 we use the surface tension, because the spreading of a liquid on a surface is a process similar to immersion or adsorption. Immersion is usually considered to effect the surface tension since no extension or contraction of the surface occurs. 

ADSA-P has been employed in various surface tension and contact angle studies, including static (advancing) contact angles [69.70], dynamic (advancing) contact angles at slow motion of the three-phase contact line [4, 71—74], and contact angle kinetics of surfactant solutions [75]. A schematic of the experimental setup for ADSA-P sessile drops is shown in Fig. 6. More details are available elsewhere [66[. 

In the absence of electrolyte it was observed that the oil droplets were large (radium about 150 ym) with a strong deformation due to gravitational effects. Very little oil was spread upon the surface in this case. But at the highest electrolyte concentration there could only be observed spread-oil, observable by the irregular three phase contact line at the air/water surface. 

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... 

It is difficult to visually observe if the three-phase contact line is receding or advancing while the droplets are allowed to stand on the surface. By calculating the contact area at the water droplet/polymer interface, it is seen that the contact area decreases in the case of Teflon and increases in the case of nylon as depicted in Figure 26.3. This implies that the droplet spreads and... 

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 26.10 A schematic representation of the meniscus shape and position of the three-phase contact line (solid/liquid/air) during immersion and emersion of a hydrophobic surface (e.g., TMS treated polymers) the dual arrows indicate which direction the beaker is moving, the small arrow on the plate indicates the direction the three-phase contact line is moving.

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.

Both hydrophobic and hydrophilic surfaces experience a transition stage at the start of the withdrawal process, seen as (C D) in Figure 26.9, and (B C) in Figure 26.12, which shows the case of hydrophilic surface. The meniscus again changes shape while the three-phase contact line remains stationary [(e f) in... 

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.

It should be noted that on the receding cycle the wet plate surface has previously interacted with water molecules for a different period of time depending on the immersion depth of the plate. Therefore, the bottom deeper immersed portions of the plate interact with the water molecules for a longer period than the shallow immersed portions closer to the top of the plate. This causes small but continuous changes in the meniscus shape even after the three-phase contact line starts to move in the advancing and receding processes. 

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