New procedure to measure simultaneously the surface tension and contact angle

This paper proposes a new procedure to simultaneously measure the static contact angle and the surface tension of a liquid using a spherical geometry. Unlike the other existing methods, the knowledge of one of both previous parameters and the displacement of the sphere are not mandatory. The technique is based on the measurement of two simple physical quantities: the height of the meniscus formed on a sphere at the very contact with a liquid bath and the resulting vertical force exerted on this object at equilibrium. The meniscus height, whose exact value requires the numerical resolution of the Laplace equation, is often estimated with an approximate 2D model, valid only for very large spheres compared to the capillary length. We develop instead another simplified solution of the Young-Laplace equation based on the work of Ferguson for the meniscus on a cylinder and adapted for the spherical shape. This alternative model, which is less restrictive in terms of the sphere size, is successfully compared to numerical solutions of the complete Young-Laplace equation. It appears to be accurate for sphere radii larger than only two capillary lengths. Finally the feasibility of the method is experimentally tested and validated for three common liquids and two "small" steel spheres.