Line Tension Measurements: An Application of the Quadrilateral Relation to a Liquid Lens System

The quadrilateral relation derived in a previous paper 1 is a generalization of the classical Neumann relation; it can be derived either from the minimum principle of free energy 1 or from the generalized theory of capillarity of Boruvka and Neumann. 2 We demonstrate that such a quadrilateral relation can be applied to line tension measurements. The experimental design involves the measurement of two contact angles and the diameter of a liquid lens system. As an example, the line tension of the three-phase contact line formed by dodecane, water, and air is found to be (−1.29 ± 0.21) × 10 - 6 J/m at the 95% confidence level, which is in the same order of magnitude as those obtained through drop-size dependence of contact angle measurements 3,4 but with the opposite sign. The negative line tension observed is found to be independent of the diameter of the three-phase contact line ranging from 1 to 7 mm, which conforms with the theoretical assumption of the formulation of the quadrilateral relation. 1 The methodology presented in this paper is believed to be simple and efficient.