Young equation contact angle

The second approach is particularly usefid and builds on the theories of interfacial tensions (Chapter 3) and concepts of contact angle/Young equation (Chapter 4) presented previously. When these theories are applied to solid-liquid interfaces and combined with Young s... 

The liquid-solid or liquidj-solid-liquidz system is both a contact angle (Young s equation) and capillary phenomena (Laplace equation). These two parameters are... 

In this section, we consider the influence of a gravitational field on the shape of a liquid droplet residing on a solid substrate (see Fig. 8). This topic was already addressed some 100 years ago by Bashforth and Adams [29], who supplied numerical tables for the shape of the liquid droplet. Their analysis is based on two equations the Laplace equation to describe the shape of the droplet, and Young s equation to determine the contact angle. Young s angle. 

The component theories, which are presented in Chapter 3, are useful for estimating the interfacial tensions of solid-interfaces (solid-liquid, solid-solid) and for characterizing solid surfaces using the experimental data for the few properties that can be measiued (liquid-gas surface tension, liquid-liquid interfacial tension, contact angle). Important equations in this context arc the Young equation... 

Equations II-12 and 11-13 illustrate that the shape of a liquid surface obeying the Young-Laplace equation with a body force is governed by differential equations requiring boundary conditions. It is through these boundary conditions describing the interaction between the liquid and solid wall that the contact angle enters. 

The preceding definitions have been directed toward the treatment of the solid-liquid-gas contact angle. It is also quite possible to have a solid-liquid-liquid contact angle where two mutually immiscible liquids are involved. The same relationships apply, only now more care must be taken to specify the extent of mutual saturations. Thus for a solid and liquids A and B, Young s equation becomes... 

The effect of surface roughness on contact angle was modeled by several authors about 50 years ago (42, 45, 63, 64]. The basic idea was to account for roughness through r, the ratio of the actual to projected area. Thus = rA. lj apparent and similarly for such that the Young equation (Eq.-X-18) becomes... 

Ruch and Bartell [84], studying the aqueous decylamine-platinum system, combined direct estimates of the adsorption at the platinum-solution interface with contact angle data and the Young equation to determine a solid-vapor interfacial energy change of up to 40 ergs/cm due to decylamine adsorption. Healy (85) discusses an adsorption model for the contact angle in surfactant solutions and these aspects are discussed further in Ref. 86. 

The axisymmetric drop shape analysis (see Section II-7B) developed by Neumann and co-workers has been applied to the evaluation of sessile drops or bubbles to determine contact angles between 50° and 180° [98]. In two such studies, Li, Neumann, and co-workers [99, 100] deduced the line tension from the drop size dependence of the contact angle and a modified Young equation... 

Since both sides of Eq. X-39 can be determined experimentally, from heat of immersion measurements on the one hand and contact angle data, on the other hand, a test of the thermodynamic status of Young s equation is possible. A comparison of calorimetric data for n-alkanes [18] with contact angle data [95] is shown in Fig. X-11. The agreement is certainly encouraging. 

The extensive use of the Young equation (Eq. X-18) reflects its general acceptance. Curiously, however, the equation has never been verified experimentally since surface tensions of solids are rather difficult to measure. While Fowkes and Sawyer [140] claimed verification for liquids on a fluorocarbon polymer, it is not clear that their assumptions are valid. Nucleation studies indicate that the interfacial tension between a solid and its liquid is appreciable (see Section K-3) and may not be ignored. Indirect experimental tests involve comparing the variation of the contact angle with solute concentration with separate adsorption studies [173]. 

To review briefly, a contact angle situation is illustrated in Fig. XIII-1, and the central relationship is the Young equation (see Section X-4A) ... 

In liquid-phase sintering, densification and microstmcture development can be assessed on the basis of the liquid contact or wetting angle, ( ), fonned as a result of the interfacial energy balance at the solid-liquid-vapour intersection as defined by the Young equation ... 

Methods of Measurement Methods of characterizing the rate process of wetting include four approaches as illustrated in Table 20-37. The first considers the ability of a drop to spread across the powder. This approach involves the measurement of a contact angle of a drop on a powder compact. The contact angle is a measure of the affinity of the fluid for the solid as given by the Young-Dupre equation, or... 

Fig. 4. Definition of contact angle showing the derivation of Young s equation, Eq.. 8, using a balance of horizontal forces at the three-phase interline.

Since —1 < cos < 1, Young s equation is valid only when the right hand side of Eo 3 or Eq. 3a lies between these limits, i.e. the observed contact angle is finite. In le event that the measured contact angle is 0°, i.e. full spreading occurs, one may conclude only that... 

Combination of Eq. 7 or Eq. 8 with the Young-Dupre equation, Eq. 3, suggests that the mechanical work of separation (and perhaps also the mechanical adhesive interface strength) should be proportional to (I -fcos6l) in any series of tests where other factors are kept constant, and in which the contact angle is finite. This has indeed often been found to be the case, as documented in an extensive review by Mittal [31], from which a few results are shown in Fig. 5. Other important studies have also shown a direct relationship between practical and thermodynamic adhesion, but a discussion of these will be deferred until later. It would appear that a useful criterion for maximizing practical adhesion would be the maximization of the thermodynamic work of adhesion, but this turns out to be a serious over-simplification. There are numerous instances in which practical adhesion is found not to correlate with the work of adhesion at ail, and sometimes to correlate inversely with it. There are various explanations for such discrepancies, as discussed below. 

A requirement underlying the validity of Zisman plots is that there be no specific interactions, such as acid-base interactions, between the solid surface and the probe liquids. Such interactions, however, can, in principle, be taken into account by Young s equation, provided the contact angle remains finite. Their... 

The phenomenon of wetting of a solid by a liquid depends on the surfaces and interfacial energies. When a liquid droplet is in contact with an ideally smooth solid surface, as shown schematically in Fig. 9, according to the Young s equation [72], the contact angle (6) of the liquid is given by... 

Fig. 9. Schematic of contact angle of a liquid on a solid. By balancing components of interfacial free energies in the horizontal direction, we can obtain the Young s equation.

Many of the most widely used methods are based on measuring the contact angles of a series of test liquids on the solid surface, and evaluating the surface energies via Young s equation, Eq. 4 above. 

For the solid-liquid system changes of the state of interface on formation of surfactant adsorption layers are of special importance with respect to application aspects. When a liquid is in contact with a solid and surfactant is added, the solid-liquid interface tension will be reduced by the formation of a new solid-liquid interface created by adsorption of surfactant. This influences the wetting as demonstrated by the change of the contact angle between the liquid and the solid surface. The equilibrium at the three-phase contact solid-liquid-air or oil is described by the Young equation ... 

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