The stability of axisymmetric menisci

Abstract

The conditions that govern the equilibrium and stability of a meniscus have been obtained from the first and second derivatives of the energy of the meniscus when it undergoes axisymmetric deformation. The energy of forming a meniscus is defined in thermodynamic terms and methods are given for calculating the free energy of a mensicus in the perturbed and unperturbed state. The stable, critically stable and unstable equilibrium states of a meniscus are all defined in terms of an energy profile, that is, the variation of energy with degree of perturbation. The variational problem of defining parameters for a critically stable meniscus is solved graphically by using a three-dimensional cluster of energy profiles, and it is shown that certain properties of the meniscus, notably volume or pressure, reach limiting values at critical conditions. Four types of stability are considered for each of three forms of axisymmetric menisci. The stability types are those limited by volume or pressure, in conjunction with limitation by the size of the supporting solid surface or the angle of contact. The three forms of menisci are pendant drops, sessile drops and rod-in-free-surface menisci. Detailed stability criteria are given for each of the twelve different combinations of stability type and meniscus form. The stability criteria of this study are all derived by numerical interpolation methods applied to the tables of equilibrium meniscus shapes - they are thus theoretical. Where possible they have been compared with experiment and with other studies, and are found to predict critically stable states with an accuracy greater than that likely to be found in the normal course of experiments.