Ranking proposed models for attaining surface free energy of powders using contact angle measurements

This study is an attempt to evaluate the applicability of various proposed mathematical models to calculate the surface free energy of commercially available powders. The capillary rise experiments were employed to achieve the contact angle between 15 powders and seven corresponding liquids by means of the modified Lucas–Washburn's equation. The surface free energy of powders was then calculated using different models inclusive of Owens/Wendt, harmonic mean, van Oss et al., combined mean (i.e. the combination of Owens/Wendt and harmonic mean models) and Li/Neumann models. Mathematical approaches were used to assess the accuracy of the calculated surface free energy and its components for different powders. A series of first-, second- and third-order functions as well as an exponential one were developed and put to test for one-, two- and three-parameter variables of liquid surface tension. Unfortunately, all such functions did not perform well in correctly estimating the contact angles of the liquid/powder systems (i.e. r2 range being 0.48–0.68 and PF/3 range being 114–312). On the other hand, a series of trained artificial neural networks (ANNs) comparatively gave good correlations, predicting with unsurpassed accuracy the contact angles of the same corresponding liquid/powder systems (i.e. r2 range being 0.93–0.94 and PF/3 range being 30–55). Therefore, the attained and tested ANNs were used further to provide the surface free energy of the 15 powders. In addition, the ANNs were also employed to rank the surface free energies of powders as well as their corresponding components as calculated by other models. The results showed that the geometric mean model was able to calculate the surface free energy of powders with more accuracy than all the other models.