The Equilibrium And Stability Properties of Menisci: The Measurement Of Surface Tension By Exact Methods

Abstract

The literature concerning the properties of menisci is briefly reviewed and it is shown that numerical analysis using computers has led to the solution of a whole range of meniscus problems. Menisci are classified and their properties defined according to the nature and number of the supporting solid surfaces and of certain shape characteristics. The sizes and shapes of different types of menisci are then obtained by integrating the Laplace—Young equation numerically. The free energy of the whole meniscus system is derived in terms of the surface area and the potential energy in the gravitational field and the equilibrium and stability given in terms of the first and second differential of the free energy with respect to perturbation. Axisymmetric perturbations only are considered as they are those of lowest energy and hence most damaging and the energy profiles of such perturbed menisci have been obtained by numerical analysis. It is shown that when critical stability is reached the size and shape of a given meniscus become unique theoretically determined properties. These critical properties have been extracted from the tables of shape and size. Finally it is shown that a further set of unique properties, but at stable equilibrium, may also be extracted from the table. These unique properties form an excellent set of conditions by which surface tension is measured with great precision. © 1976, Walter de Gruyter. All rights reserved.