B Adhesional Wetting

The equation is from Dupre (1869). In this process any reduction of the interfacial tension between substrate and the wetting liquid results in an increased tendency for adhesion to occur, but reduction of either the surface tension of the liquid or the surface tension of the substrate decreases the tendency of adhesion to occur. This accounts for the poor adhesion of substances to low-energy surfaces, especially when the natures of substance and substrate are very different (i.e., ySL is large). 

The difference between the work of adhesion of the liquid for the substrate and its work of cohesion equals the spreading coefficient Sus - 

Therefore, if Wa Wc, the spreading coefficient is positive, 0 = 0°, and the liquid spreads spontaneously over the substrate to form a thin film. If Wa Wr, the spreading coefficient is negative, 0 is greater than zero, and the liquid does not spread over the substrate but forms droplets or lenses with a finite contact angle. 

When the work of adhesion equals the work of cohesion, 

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