Lens size dependence of contact angle and the line tension of the dodecane-water-air system

Abstract

Line tension is calculated by applying the contact line quadrilateral relation to a dodecane-water-air liquid lens system, where two contact angles are measured through an image analysis scheme. To complement previous measurements on individual lenses [1], contact angles were determined as a function of lens diameter. In order to exclude the possibility of any fluid mechanics or other dynamic effects, the change of lens size was performed at three different rates. No apparent rate dependence of contact angle and line tension can be observed for the three speeds. By reformulating the quadrilateral relation, the lens-size dependence of contact angles can be used in the calculation of line tension. To compute line tension with this scheme, three derivatives need to be obtained in addition to two contact angles and three surface tensions. No computational advantage can be gained over the direct application of the quadrilateral relation; however, the approach used here provides a potentially important approximation in term of a single surface tension and a lens-size dependent contact angle. For the water-dodecane system studied here, the line tension values calculated, by the quadrilateral relation, its reformulation and the simplified quadrilateral relation, are negative and between −1 and −4 × 10 −6 J m −1.