Young and 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). 

The size of the contact angle depends on the magnitude of the liquid-solid adhesive force compared with that of the liquid-liquid cohesive force. Specifically, Young s equation (also called the Young and Dupre equation) indicates that... 

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. 

Such observations suggest that while the one can always be viewed as the mathematical construct of the other, surface free energy is a more rational quantity than surface force in the context of a contact angle situation. The former has also the merit of carrying some specific implications. The Young and Dupre equation is obtained by setting... 

The conclusion at this point is that it is futile to seek a general thermodynamic connection between contact angle and the surface free energy of the pure solid. Any success in relating-lhe two must come from theory based on specific molecular models. In this respect, then, the writers deny thermodynamic value to the Young and Dupre equation. 

Just as it was interesting to verify experimentally the Gibbs adsorption equation in the case of solution-vapor interfaces [26], it should be worthwhile to verify such aspects of the Young and Dupre Equation 1 as are experimentally accessible. The approaches outlined above are not thermodynamic in the sense that particular molecular models are... 

With respect to purely thermodynamic tests of the Young and Dupre equation, a study of the temperature dependence of contact angles, combined with calorimetric and surface area measurements, offers some promise. This would provide a classical second law test. 

If this approximation is accepted, the Young and Dupre equations may be again introduced in O Eq. 6.20b yielding... 

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

It may be obvious to relate the equation of Young and Dupre (Equihion 8.3) to the Gibbs energy of adhesion between S and L It follows from Equation 5.11... 

Estimation of Thermodynamic Parameters from Contact Angle Measurements 23.2.3.1 Equations of Young and Dupre... 

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... 

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. 

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 ... 

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 ... 

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... 

In order to calculate polymer/filler interaction, or more exactly the reversible work of adhesion characterizing it, the surface tension of the polymer must also be known. This quantity is usually determined by contact angle measurements or occasionally the pendant drop method is used. The former method is based on the Young, Dupre and Eowkes equations (Eqs. 21,8, and 10), but the result is influenced by the surface quality of the substrate. Moreover, the surface (structure, orientation, density) of polymers usually differs from the bulk, which might bias the results. Accuracy of the technique maybe increased by using two or more liquids for the measurements. The use of the pendant drop method is limited due to technical problems (long time to reach equilibrium, stability of the polymer, evaluation problems etc.). Occasionally IGC is also used for the characterization of polymers [30]. 

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). 

The wetting of a hydrophobic solid surface by an aqueous medium is considerably helped by the addition of surface-active agents. Wa is increased and yLG is decreased (Figure 6.4b), so that, from the Young-Dupre equation, 0 is reduced on two counts. 

The variation of contact angle with orientation of surface planes can be understood by considering the Young-Dupre equation and the definition of Wa based on the simple model of Section 1.1 ... 

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