Dupre’s equation

The work of adhesion between two liquids orientation at liquid-liquid interfaces. Much the clearest conclusions at present available as to the structure of the surfaces of liquids (except those covered by films of another substance) concern the interface between two liquids. They have been obtained by considering the work of adhesion between the liquids, or the perpendicular attraction across the interface. This work of adhesion can be ascertained by measurement of the surface tensions of the two liquids separately, and of the interfacial tension between them, and applying Dupre s equation (Chap. I, 8) ... 

The values of the adhesional work between the two liquids and the solid, and WB8, are given by Dupre s equation... 

By definition, Wad is the sum of surface free energies of a liquid (Fiv) and a solid in vacuum (F8) minus the interfacial free energy (Fsl) according to Dupre s equation ... 

The term yg in Equation 1 needs clarification. As Bangham and Razouk [6] pointed out, the vapor of the liquid will be adsorbed on the solid surface, often considerably decreasing its surface free energy. In Equation 1, and also in Dupre s Equation 3,... 

In the absence of chemisorption and interdiffusion, the work of adhesion is the sum of the various intermolecular forces involved and can be related to the surface free energies (Dupre s equation) ... 

A second relation between the three forces is obtained using Dupre s equation, defining the reversible work 1 2,3 needed to separate a unit area of the solid liquid interface. Conservation of energy requires that [17]... 

Besides the capillary length, another key figure of merit is the work of adhesion (W a)-It describes the amount of work necessary to lift a droplet off the surface, hence it is associated with overcoming the surface-liquid interactions. values can be calculated using Dupre s equation [24] ... 

By measuring the contact angles between the polymer and various liquids, it is possible to calculate the proportion of surface energy effect in the initial retractive stress using Young-Dupre s equation, the value is around 0.3 After six minutes of relaxation, it increases to 0.5 ... 

Oi2 vanishes, and two new surfaces with surface free energies Oj and Oj, respectively, are formed. The energy balance of this process is given by Dupre s equation and can be written as follows ... 

By combining Young s equation with Dupre s equation, one gets... 

Contact Angle, Dupre s Equation, and Neumann s Triangle... 

In the last century Dupre obtained another relationship between ogi, agg, and aig in terms of the work, unit area of the liquid-solid interface. Consider a unit area of a liquid-solid surface (Fig. 1.20). Now, the energy of a unit area of interface plus the work done in separating the surfaces must be equal to the final energy of the unit areas of the solid surface and the liquid surface after they have been separated and are in contact with the gaseous phase. Thus using energy conservation Dupre s equation is obtained,... 

It is known [16] that the wetting force of liquids increases with increase in their adhesion to the surface as well as with decrease in their cohesion energy. Taking into account Dupre s equation, inequality Eq. (12.1) may be written in the following form ... 

Finally, by substituting for the interfacial tension from the modified Young s equation (Eqn (3.12)) into the work of adhesion (Eqn (3.20)) for a solid—liquid system, the equation for the work of adhesion can be simplified to Eqn (3.21), also known as Young— Dupre s equation. 

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