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

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.

Automated summary

In this study, the effect of gravity on the capillary force, meniscus shape, and residual liquid volume of a vertical liquid bridge was systematically investigated using mathematical models and experimental validation. Feasible calculation methods were proposed for the meniscus shape and residual liquid volume on the sphere.