# Fowkes method

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 dispersive part and a non-dispersive part.

## Background

According to Young’s equation, there is a relationship between the contact angle θ, the surface tension of the liquid σ_{l}, the interfacial tension σ_{sl} between liquid and solid and the surface free energy σ_{s} of the solid:

In order to be able to calculate the surface free energy from the contact angle, the second unknown variable σ_{sl} must be determined.

In the Fowkes method, the interfacial tension σ_{sl} is calculated based on the two surface tensions σ_{s} and σ_{l} and the similar interactions between the phases. These interactions are interpreted as the geometric mean of a dispersive part σ^{D} and a non-dispersive part σ^{nD} (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 dispersive part is calculated first with the help of at least one purely dispersive liquid. The non-dispersive 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-dispersive 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.

## Bibliography

F. M. Fowkes, Attractive Forces at Interfaces. In: Industrial and Engineering Chemistry 56,12 (1964), P. 40-52.