Interfacial tension measurements using a new axisymmetric drop/bubble shape technique

This paper introduces a new mathematical model that is used to compute either the interfacial tension of quiescent axisymmetric pendant/sessile drops and pendant/captive bubbles. This model consists of the Young-Laplace equation, that describes interface shape, together with suitable boundary conditions that guarantee a prescribed volume of drops/bubbles and a fixed position in the capillary. In order to solve the problem numerically, the Young-Laplace equation is discretized by using numerical differentiation and the numerical solutions are obtained applying the well-know Newton method. The paper contains a validation of the new methodology presented for what theoretical bubble/drops are used. Finally, some numerical results are presented for both drops and bubbles of water as well as several surfactant solutions to demonstrate the applicability, versatility and reproducibility of the proposed methodology.