Capillary Bridges between Two Spherical Bodies

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.