Capillary Bridges between Two Spherical Bodies

TLDR

A method was devised to measure capillary forces from microscopic pendular liquid bridges, and closed‑form approximations were derived to compute forces between equal and unequal spheres as functions of separation, bridge volume, and contact angle, as well as to predict rupture distances for unequal spheres. Experiments on perfectly wetting bridges between spheres of equal and unequal radii confirmed that the developed method accurately matches numerical Laplace–Young predictions, revealed that gravitational distortion criteria are overly restrictive, showed negligible disjoining pressure effects, and found the Derjaguin approximation to be reasonably accurate for small bridge volumes and moderate separations.

Abstract

A method was developed for measuring the capillary forces arising from microscopic pendular liquid bridges. Results are described for perfectly wetting bridges between spheres of equal and unequal radii. A comparison with the theoretical values calculated from a numerical integration of the Laplace−Young equation demonstrated the accuracy of the method. It also showed that existing criteria for gravitational distortion are too restrictive and that the influence of the disjoining pressure is negligible. The Derjaguin approximation for spheres of unequal size was shown to be relatively accurate for small bridge volumes and for separation distances excluding those at close-contact and near-rupture, which correspond to maxima in the filling angle. Closed-form approximations were developed in order to conveniently calculate the capillary forces between equal and unequal spheres as a function of the separation distance and for a given bridge volume and contact angle. A closed-form approximation was also developed to calculate the rupture distance for liquid bridges between spheres of unequal sizes.