Relation between equilibrium contact angle

The relation between equilibrium contact angles at a solid surface, and the adhesion between solid and liquid, is reviewed. The information deducible as to the chemical nature of the groups exposed at the surface is summarized. 

Wetting of a surface by a fluid is controlled by the Young Equation (Eq. 12.1), which relates the equilibrium contact angle (0) of the fluid (Figure 2.12) to the interfacial tensions (-y) between the liquid and vapor (LV), the solid and the vapor (SV) and the solid and the liquid (5L). 

Assuming that the Laplace pressure is the same everywhere within the rim (i.e., the same curvature is assumed to exist everywhere in the rim) requires that dyn 0- For thin films in the nanometer range and a size of the rim in the range of micrometers, the logarithmic factors at positions R and F are similar. Consequently, a highly useful relation is obtained between dynamic and equilibrium contact angles for the case of viscous dewetting (with 4>) [136] ... 

Contact Angie. The degree to which a liquid wets a solid is measured by the contact angle B (Fig 6). When 6 = 0, the liquid spreads freely over the surface and is said to completely wet it. This occurs when the molecular attraction between the liquid and solid molecules is greater than that between similar liquid molecules (54). Surface tensions are related to the contact angle by an expression from equilibrium considerations (55) ... 

On the nanoscale the shape of such droplets can deviate significantly from the macroscopic shape of a spherical cap due to the finite range of the intermolecular interactions involved. As described later, one can actually relate the macroscopic equilibrium contact angle, the character of wetting transitions, and the shape of nanodroplets to the intermolecular interactions by using, for example, classical density functional theory (DFT). But the long range of intermolecular interactions also affects the motion of droplets. In particular it can lead to lateral interactions between droplets and structures, which are absent on the macroscopic scale. 

Of relevance is Young s equation, which relates the interfacial tension between the surfactant solution and oil (yow), oil and solid substrate (yos) and surfactant solution and solid substrate (yws) to the equilibrium contact angle 0 ... 

Fig. 14. Schematic illustration of a drop ofliquid spreading in contact with a solid surface, showing the relations between the relevant parameters the contact angle, 0 the solid/vapor interfacial free energy, Ysv the liquid/vapor interfacial free energy, yLV and the solid/liquid interfacial free energy, ySL. Young s equation describes the relationship between these parameters for a stationary drop at thermodynamic equilibrium [175]...

This report is concerned with contact angle hysteresis and with a closely related quantity referred to as "critical line force (CLF)." More particularly, it is concerned with the relationship between contact angle hysteresis and the magnitude of the contact angle itself. Two sets of liquid-solid-vapor systems have been investigated to provide the experimental data. One set consists of Teflon [poly(tetrafluoroethylene), Du Pont] and a series of liquids forming various contact angles at the Teflon-air interface. The second set consists of polyethylene and a similar series of liquids. In neither case was the ratio of air to test liquid vapor at the boundary line controlled, but it can be assumed that the ambient vapor phase operative in all the systems was close to an equilibrium mixture. 

The wetting behavior of polymers is reviewed beginning with the thermodynamic conditions for contact angle equilibrium. The critical surface tension of polymers is discussed followed by some of the current theories of wettability, notably the theory of fractional polarity and theories of contact angle hysteresis. The nonequilibrium spontaneous and forced spreading of polymer liquids is reviewed from two points of view, the surface chemical perspective and the hydrodynamic perspective. There is a wide di.sperity between these two viewpoints that needs to be resolved inorder to establish the predictive relations that govern spreading behavior. 

Of the driving forces for capillary action mentioned above, the most fundamental are those of interfacial tension and related effects (e.g., contact angle). As pointed out in Chapter 2, a liquid-fluid interface behaves as if it is an elastic film stretched over (or between) the two phases and resisting any more stretching to produce greater interfacial area. The tension results fundamentally from the imbalance in the forces acting on the molecules at the interface, which tend to pull the molecules back into the bulk phases. At equilibrium, the surface... 

A simple experimental evidence of surface modification, for instance concerning the hydrophilic/hydrophobic balance of the surface, can be searched for. To do this, the simplest and oldest method measures the contact angle at equilibrium between the clean surface of a material, a liquid and its vapour. This method permits evaluation of the surface tension of material surfaces, which can be related to the hydrophilic/hydrophobic balance. Several experimental processes have been described, but the simplest is deposition of a droplet of liquid on the surface, as shown in Eigure 2.18. 

While Figure 12.2 relates to the equilibrium situation, more can be learned by a study of such droplets in motion on the surface. Consider the droplet on an inclined plane. Then there are two contact angles, the advancing contact angle and the receding contact angle. There are three main causes of the hysteresis between the two angles ... 

The Young-Dupre relation is the boundary condition that allows the determination of the shape of the surface between two fluids in contact with a solid wall, such as a liquid drop on a solid wall within a gas (dew) or an air bubble adhering to a sohd wall within a liquid. It is important to emphasize that the Young-Dupre law is applicable only to the case where the triple line is at static equilibrium on the sohd. When the triple line moves (if for example the dew drop slides down the wah), the concept of dynamic contact angle shoirld be substituted for that of static contact angle for better results. ... 

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