Method according to Wu

The method according to Wu (Wu method) is a method for calculating 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 polar part and a 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.
Building on the Fowkes method, the interfacial tension σsl is calculated based on the two surface tensions σs and σ and the similar interactions between the phases. These interactions are interpreted as the harmonic mean of a disperse part σD and a polar part σP of the surface tension or surface free energy:

At least two liquids with known disperse and polar parts of the surface tension are required to determine the surface free energy of the solid, wherein at least one of the liquids must have a polar part > 0.
When carrying out the calculation, an equation is set up for every possible combination of two liquids - n liquids result in (n2-n)/2 equations with correspondingly many partial results. The resulting surface free energy is the arithmetic mean of the partial results.
Interfacial tension measurements between polymer melts, i.e. materials with predominantly low surface tension of the individual phases, form the empirical basis of the method. Accordingly, the Wu method for calculating surface energy is mostly used for polymers with low surface energy (up to 40 mN/m).


S. Wu, Calculation of Interfacial Tensions in Polymer Systems. In: J. Polym. Sci. 43 (1971), P.19-30.
S. Wu, Polar and Nonpolar Interaction in Adhesion. In: J. Adhesion 5 (1973), P. 39-55.