Mathematical study on gravity effect of the liquid bridge between two rigid spheres

Abstract

To better understand how gravity affects the evolution of capillary force and meniscus shape of the vertical liquid bridge between two millimeter-size spheres, an explicit mathematical model was built using Surface Evolver software. In this study, the rupture behavior of liquid bridge in the equilibrium state was studied using the energy minimization method, and the validity of the mathematical method followed was verified by comparing with existing research results. In addition, the gravity effect on the meniscus shape and geometric parameters were systematically studied. Finally, the gravity effect on the residual liquid volume after the liquid bridge ruptures was examined, and a calculation method for the residual liquid volume on the sphere was proposed, which was proven by mathematical methods and experiments. The relative error was <16% when the liquid dripping error was neglected, proving the feasibility of the calculation method.