The Fowkes method is used to calculate the surface free energy of a solid from the contact angle with several liquids. In doing so, the surface free energy is divided into a disperse part and a non-disperse part.
According to Young’s equation, there is a relationship between the contact angle θ, the surface tension of the liquid σl, the interfacial tension σsl between liquid and solid and the surface free energy σs of the solid:
In order to be able to calculate the surface free energy from the contact angle, the second unknown variable σsl must be determined.
In the Fowkes method, the interfacial tension σsl is calculated based on the two surface tensions σs and σl and the similar interactions between the phases. These interactions are interpreted as the geometric mean of a disperse part σD and a non-disperse part σnD (not described by Fowkes in more detail) of the surface tension or surface free energy:
The surface free energy of the solid is determined from the contact angle data in two steps: The disperse part is calculated first with the help of at least one purely disperse liquid. The non-disperse part is then determined with at least one further liquid with polar parts.
With this second step, the Fowkes method goes beyond the original literature and follows a similar path to the Owens, Wendt, Rabel and Kaelble method (OWRK). The latter defines the non-disperse part as a polar part, and on account of a different calculation process it requires only two liquids. The OWRK method is used more frequently in practice than the Fowkes method.
F. M. Fowkes, Attractive Forces at Interfaces. In: Industrial and Engineering Chemistry 56,12 (1964), P. 40-52.