The equilibrium and stability of menisci between touching spheres under the effect of gravity

The equilibrium shapes and stability of menisci formed at the contact point between two vertically aligned spheres were theoretically studied. The equilibrium configurations were determined as solutions of the equation of Young-LaPlace. The stability of the equilibrium shapes was determined by means of a perturbation analysis of the three-dimensional form of the equation of Young-LaPlace. It was found that there is a maximum amount of liquid that can be retained at the contact point, which is determined by geometrical considerations when gravitational effects are important, and by the onset of instability when gravitational effects are negligible. The maximum amount of liquid diminishes as the gravitational forces become stronger with respect to surface tension forces. In the case of small contact angles, an increase in the contact angle results in an increase in the maximum liquid retention, whereas, when the contact angle is large, this trend is reversed.