Liquid bridges between spheres in a gravitational field

Abstract

A theoretical study has been made of the properties of a liquid bridge between spheres of equal and unequal radii taking into account the effect of gravity on the meniscus shape and capillary attractions. The interfacial shape of the bridge is obtained by a numerical solution of the Young-Laplace equation employing the Runge-Kutta method for a given sphere pair, liquid bridge volume, and contact angle. The capillary force, sphere separation, minimum neck diameter, and filling angle of the liquid on both spheres are calculated numerically for interfacial shapes which exhibit the minimum neck diameter. The equal bridge volume problem at different sphere separations for a given set of spheres is solved with the two point boundary-value condition which must be satisfied on the sphere surfaces. This new solution, which takes into consideration gravitational disortion, enables large spheres to be used in experimental studies, and permits accurate measurements of the bridge volumes and the maximum amount of liquid that can be deposited between the spheres in a given system. It is found that the capillary attraction and maximum liquid bridge volume increases as the contact angle decreases and, also, as the radius of the bottom sphere increases. The effects that changing the bridge volume, sphere radii, and contact angle have on the capillary force, the maximum sphere separation, and other factors affecting the system are investigated.