Vector methods and matrix equations applied to symmetric expressions for three-component surface tension determination

Despite its potential usefulness, the Lifshitz-van der Waals/acid–base approach is a controversial method for surface tension measurement in the physical engineering community, due to its apparent inconsistencies. In the present work, a vector method using matrix equations is studied for desirable test liquid screening, rearranging a commonly used governing equation into symmetric forms. Additionally, a new geometric perspective using vector volumes is proposed as a simple measure for selecting a set of test liquids, and compared to a state-of-art method that relies on the condition number of a matrix containing the liquid surface tension components. It is found that these two approaches agree to a high degree. On the other hand, a commonly stated approach of using a high number of test liquids is critically discussed in terms of practical applicability. The method presented for calculating solid surface tension values is further extended for calculating surface tension components of an unknown liquid, using known solid surface tension components.