Menisci at a free liquid surface: surface tension from the maximum pull on a rod

Abstract

The maximum force on a vertical rod supporting a stable meniscus, at equilibrium, formed at the free surface of a liquid, is shown to be a characteristic property of the system. This maximum force depends only on the rod radius, the density of the liquid, the gravitational acceleration and the surface tension. The maximum force represents the product of the maximum volume of liquid held above the general level, the gravitational acceleration and the density. The maximum volume of the meniscus has been derived theoretically as a function of rod radius in the form of a parametric equation with a table of coefficients. Thus from the measured rod radius and maximum force, the surface tension is derived. The surface tensions of water and of other liquids have been measured using this method and are found to agree very well with other methods given in the literature. However, this method is believed to be accurate to ±0.1 mN m^–1, and it is an absolute method in that it requires no arbitrary end corrections involving a prior knowledge of the surface tension. It is important that the rod should be level and have a radius not so large that the angle of contact became a limitation on the maximum force measurable. The method does not involve detachment of the rod from the surface. It is an equilibrium method the position of which may be approached from both directions.