Interfacial tensions, contact angle and wetting

Before we proceed to discuss either the experiments that can give information about surface or interfacial tension, or the statistical mechanical theories allowing more precise predictions of these quantities, we should discuss some of the fundamentals of classical interfacial thermodynamics. The interested reader will find a fuller account in the book by Adamson (1990). 

Thermodynamically the interfacial tension between two phases may be defined as the increase in Gibbs free energy of the whole system per unit increase in interfacial area, carried out under conditions of constant temperature and pressure, that is 

This definition of interfacial tension also encompasses surface tension, in which the two phases are the pure liquid and its coexisting vapour. If we define the interface between two phases, A and B, as a region of finite thickness, t, where the composition changes from that comprising A in the bulk phase to the bulk phase B, then the chemical potential of any species must be equal in the two phases and at the interface  

For each of the phases the most general expression for the Gibbs free energy is 

Subtracting the general variation of the Gibbs free energy in the interfacial region from the total differential of equation (2.2.5) and dividing by the interfacial area gives 

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