Dupre equation

Equation X-17 was stated in qualitative form by Young in 1805 [30], and we will follow its designation as Young s equation. The equivalent equation, Eq. X-19, was stated in algebraic form by Dupre in 1869 [31], along with the definition of work of adhesion. An alternative designation for both equations, which are really the same, is that of the Young and Dupre equation (see Ref. 32 for an emphatic dissent). 

By relating the work required to force a volume dp" of mercury into the pore of a solid to the work required to form an element d/4 of mercury-solid interface, and making use of the Young-Dupre equation (3.70) one arrives at the expression... 

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... 

Substitution of Eq. 3 into Eq. 1 leads to the Young-Dupre equation ... 

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. 

The process of viscoelastic braking just described has certain parallels with the dynamic adhesion of elastomers. When, for example, a rubber strip is peeled from a rigid substrate, the effective, or apparent, work of adhesion, W, is usually much greater than the intrinsic, or reversible, energy of adhesion, Wq, given by the Dupre equation [15] ... 

Using the Young-Dupre equation, W = y(l + cos 0), and introducing the boundary condition of 0 = 0o for t = 0 (no swelling) and 0o , (contact angle at equilibrium with swelling), we obtain ... 

These considerations can also be used to derive the Dupre equation, where AG(s) is the Gibbs energy of adsorption of the solvent per unit area of the metal surface ... 

Equation (6.39) was first derived by Young, and is often referred to as the Young-Dupre equation. We usually distinguish between full (6< 90°) and partial wetting (0 > 90°) and an alternative measure of the same property is given by the wetting coefficient ... 

Wettability Dependence of Detergency. The dependence of Dr on i]/ was described above. The purpose of this section will be to develop an expression for in terms of experimentally accessible interfacial tension quantities. To begin with, the TPL has a geometry as shown in Figure 7. For this system, the Young-Dupre"" equation (14-16) can be written as... 

Using the value of Yfs the quantity Yfw can be calculated from the Young-Dupre" Equation 14. 

Wetting can be quantitatively expressed in terms of the thermodynamic work of adhesion, Wa. of a liquid to a solid using the Dupre equation... 

Combining Eqs. (2.1) and (2.2) yields the familiar Young-Dupre equation... 

The subscript s indicates the hypothetical case of a solid in contact with a vacuum. The importance of impure surfaces is well recognized in areas like brazing where the difficulty of brazing aluminum is associated with the presence of an oxide film on the surface. Therefore, Eq. (2.5) can be substituted in Eqs. (2.1) and (2.2) by introducing the spreading pressure. The Young-Dupre equation is then modified to... 

This result was qualitatively proposed by Thomas Young in 1805 and is generally known as Young s equation. It is also known as the Young-Dupre equation or the Dupre equation (MacRitchie 1990). 

What is the Young-Dupre equation What are the approximations made in its derivation Discuss the merits of those approximations. 

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