Young-Dupre relationship

The Dupre equation plays a central role in the study of adhesion. Combining Young s equation (equation (7.7)) with the Dupre equation (equation (7.15)) provides the Young-Dupre relationship, as follows ... 

Equations (5.3.1) and (5.3.2) yield the Young-Dupre relationship between the work of adhesion and the wetting angle ... 

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. 

Equations 29 and 33 combine to give the Young and Dupre relationship. 

This Young-Dupre equation allows one to determine the work of adhesion from a simple measurement of the contact angle and the liquid surface tension. Much of the experimental work in adhesion science has centered around the relationship of these two parameters. 

A further extension of these energy relationships, the Young-Dupre equation, ... 

From the Young-Dupre equation in Eq. (7.4), the relationship between contact angle and the surface tension components can be written as... 

The Young and Dupre equation for the angle of contact of a liquid resting on a solid surface may be derived as a thermodynamic relationship, but the testing of its validity for the real situation of a nonequilibrium and usually heterogeneous surface presents difficulties. These are discussed first in terms of two simple molecular models and secondly in terms of thermodynamic relationships that should permit an independent verification of the contact angle relationship. 

This may be simplified by the use of the adhesion tension relationship of Young and Dupre [cit. 30]... 

---