Analytical derivation of a pH dependent contact angle equation and the relationship to industrial processes of energy concerns

Abstract Regarding Young's equation, three fundamental interfacial energies of interfacial tensions can be identified. One of these interfacial energies relevant to our purpose is that related to the solid-liquid interface and it can be pH dependent. Intermolecular theory of surface tension links the solid-liquid interfacial tension or energy to surface charge species of solids. These species are electrostatic and depend on the pH of the aqueous medium in contact with the solid surface. Therefore, a theoretical relationship between contact angle and pH of some kind is worth exploring based on the fundamental theories of pH dependent solid-liquid interfacial tension, given the pH dependent electric double layer. A review of the literature dealing with the pH-dependent contact angle shows that polynomial curves have been fitted to contact angle versus pH data. Based on established theoretical works dealing with surface charge theories related to the electric double layer found in the literature, we have derived a pH dependent contact angle equation that describes trends in published experimental data with a high degree of regression coefficient. We have also theoretically and experimentally validated our model. The industrial significance of our model lies in the fact that the solution for pH, when the derivative is equated to zero, gives the point of zero charge pH of solid surface, which is an approach that has already been used in published works without any theoretical justification. The relationship of our model to industrial operations of energy and environmental significance has been discussed.