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) x 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.