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 kO.1 mN m-I, 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.Gay-Lussac,' attempted to determine the surface tension of a liquid by the measurement of the maximum force exerted on a horizontal plate as it was pulled away from the free flat surface of a liquid. He realised it was necessary to use a large plate (1 18.4 mm diameter) and he assumed that the meniscus formed at the edge of the plate approached that of cylindrical symmetry : in fact he assumed that the angle of the meniscus with the underside of the plate was zero.These experiments captured the attention of Young,' L a p l a ~e , ~ P o i ~s o n , ~ Kir-~h o f f , ~ Cantor,6 Lohn~tein,~ Gallenkarnpp8 Quincke, Ferguson,lO Bouasse '' and Bakker,12 all of whom attempted to obtain a relation between the force on the rod or plate, the radius of the plate and the surface tension of the liquid. Of these studies only that of Lohnstein reveals the understanding necessary to obtain this relation.The measurement of surface tension with solids of other shapes, such as the Du Nouy ring l 3 has been studied by Freud and Freud,14 and Harkins and Jordan,ls and the sphere has been studied by Huh and Mason The sphere problem also arises in flotation studies,l87 l 9 and equations used in these studies are identical with those used in surface tension measurement.However, despite this extensive area of previous investigation it appears that the solution to the rod or plate problem has not been established previously.In this study we attempt to set out the physical conditions that govern the maximum pull on a rod as it is drawn from the free surface of a liquid to form a stable meniscus. We then show that the force reaches a stable maximum value well before breakaway occurs, and that ...

A method for the direct measurement of surface tension of collected atmospherically relevant aerosol particles using atomic force microscopy

“…(3) (Padday et al, 1975) was used, using the force reading at the point the nanoneedle broke from the sample. This corresponds to point 5 in Fig.…”

Sphere tensiometry: an evaluation and critique

“…As we will see, the method holds considerable promise, but several difficulties must first be surmounted. For given R and do, therefore, [2] to [5] provide equilibrium relations between D and K.…”

“…Whereas the ring and plate both form menisci with complicated shapes, a sphere does not, thus making it ~o s s i b l e to calculate the eauilibrium interfacial force rigorously and in a relatively straightforward manner (I). The use of another simple geometry, a circular cylinder vertically protruding through the interface, and of a cylindrical tip with a sharp edge to which the meniscus attaches has also been proposed (2). Because of difficulties of vertical alignment, axisymmetry (required by the theory) may not be exactly realized with cylinders; a sphere presents no such problem.…”

Application of a Pull on a Disk Method to Measure Surface Tension of Liquids

“…Padday et al (11) have thoroughly investigated the surface tension measurement of liquids from the maximum pull on a rod. Our study on the calculation of surface tension from the maximum pull on a disk is derived from their work.…”

“…Ultimately, it was determined that the linear relationship found for rings reasoned probe ring geometry to be the most suitable method for the measurement of surface tension. However, as an alternative approach, Padday et al (11) previously determined the physical aspects governing the maximum pull on a rod. They found that the maximum force used to suspend the liquid underneath the rod, expressed as volume, is a characteristic property of the system that can be numerically correlated to the probe radius in order to determine surface tension.…”