Triple contact line

Developing the analogy in our impact problem with a hydrophobic surface, we identify the wetting phase as air, so that the static contact angle with respect to the wetting phase is defined as o = (rt — %) and the triple contact line becomes no longer stable above u a (rr — 0o) - Furthermore, v is fixed by a critical capillary number Ca = u 7l/tlv that evolves like Ca l/9 . 

Fig. 13. Moving triple contact line, three different regions characterize the flow.

If we assume a spherical cap geometry for the heavy DCM drop, the forces acting on the triple contact line can be represented by the Neumann triangle as shown in Fig. 5. The corresponding young equation reads 7w/a = 7o/a+7w/o cos 0. 

Liu J, Mei Y, Xia R (2011) A New wetting mechanism based upon triple contact line pinning. Langmuir 27 196-200... 

This set of conditions is the one that is satisfied at large distances from the triple point in the Seppecher s phase field equations for the contact fine motion as in the phase field equations, our model assumes an unhindered interface motion, without caring for the heat transfer due to the latent heat. It also provides a theory consistent with the balance of normal stress across the fluid/fluid interface. The idea presented here opens the way to model fluid mechanical problems with contact line motion. This is something that is impossible with the Huh-Scriven solution without balancing the normal stress one... 

Fig. 11.1 (a) Craitact-mode AFM deflection images of PS in water. The presence of nanobubbles is obsCTved. Occasionally the bubbles are removed by the effect of the tip only a portion of the nanobubble appears in the image white arrows), (b) Schematic representation of a nanobubble in a water/polymer interface. The contact angle 0 is determined by the equilibrium between the horizontal forces in the triple solid-liquid-vapor contact line liquid-vapor 71.v, solid-liquid 75.1, and solid-vapor 75. interfacial tensions. The vertical component of the liquid-vapor interfacial tension, 71. sin(0), is equilibrated by a deformation of the substrate, as described in the text... 

Our steering results are demonstrated using an experimentally validated numerical model [20] of droplet motion inside the UCLA electrowetting system [21, 22], This model of EWOD fluid dynamics includes surface tensimi and electrowetting interface forces, viscous low Reynolds two-phase fluid flow, and the essential loss mechanisms due to contact angle saturatimi, triple point line pinning, and the related mechanism of contact angle hysteresis. 

In this classical forced wetting situation, it has been shown, by expressing a force balance on the triple line, that this contact line becomes unstable above a critical value 0 of the putting velocity, associated with a constant capillary number Ca = vlm lYvsi (with t 15-20 a numerical factor [52, 53]). This in-... 

Wetting is defined as the process whereby a liquid when brought into contact with a solid displaces some of the fluid phase so that a stable triple-phase line of contact is formed, as seen in Fig. 1. Spreading, also described in Fig. 1, is the process whereby the liquid, once in contact with the solid, displaces the third phase completely from all parts of the surface and at the same time creates a new liquid-air (third phase). Finally, one describes the process of dewetting (or spontaneous dewetting) as that wherein the third phase, usually a liquid, itself spreads and displaces completely the first liquid from the solid surface. 

FIGURE 3.7. Relaxation of a line of triple contact pinned at defects (after Garoff and Decker)- (A) before displacement (B) after a displacement of 500 pm. 

While it is intuitive that water-repellency and self-cleaning are related to each other, because the ability to repel water is related to the abifity to repel contaminants, it is difficult to quantify self-cleaning. As a result, a quantitative relation of the two properties remains to be estabfished. A quahtative explanation of the selfcleaning was proposed by Barthlot and Neinhuis, who suggested that on a smooth surface, contamination particles are mainly redistributed by a water drop, whereas on a rough surface they adhere to the drop and are removed from the leaves when the drop rolls off A detailed model of this process has not been developed, but, obviously, whether the particle adheres to the drop depends upon the interactions at the triple line (liquid-solid-air contact line) and on whether the magnitude and direction of the surface force allows the particle to be detached from the surface and flown away (Fig. 3). 

Fourth, for a small drop and curved triple lines, the effect of the contact line tension may be significant. Molecules at the surface of a liquid or solid phase have higher energy because they are bonded to fewer molecules than those in the bulk. This leads to surface tension and surface energy. In a similar manner, molecules at the... 

The position of the mercury meniscus in the capillary depends on the surface tension between the mercury and the sulphuric acid and this, in turn, depends on the electrical potential between the mercury and the acid. If this potential is altered, as, for example, by connecting the two mercury electrodes with a cell or with two points of a circuit between which there is a difference of potential, the meniscus will movej and for small differences of potential, the amount of movement is proportional to the difierence of potential. In order, however, that the meniscus shall take up a definite position, the two electrodes must be connected together except when making a measurement This is efiected by means of a triple contact Morse key, shown in Fig. 72. The electrical connections between the terminals a, b, c and the contacts d, V, d are indicated by means of the dotted lines. The electrodes of the electrometer are connected with the terminals b and c, so that they are connected together when the key is in its normal position. The terminals a and c are connected with the rest of the circuit, so... 

Equilibrium at the triple line satisfies Young s equation [Eq. (1)], but if the contact angle as a function of time, 0(0, is greater than 6o, then there is a net spreading force acting per nnit length of triple line and given by [5] ... 

It has been shown that the kinetics of the spreading of a liquid on a rubber is largely dependent on viscoelastic dissipation in the wetting ridge of the substrate near the triple line. This behavior may, in practice, be slightly altered by moderate swelling that modifies the solid/liquid interactions for long contact times. 

The predominant form of released petroleum products is a liquid that is immiscible with water this is called the free product (in this section it will be referred to as oil). The behavior of water and oil in soil depends on the interaction of the three phases water, oil, and soil. The affinity of water or oil with the soil can be estimated by establishing the contact angle of oil/water/soil triple line. 

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