Modeling the Evolution and Rupture of Pendular Liquid Bridges in the Presence of Large Wetting Hysteresis

A model has been developed to predict the shape evolution, rupture distance and postrupture liquid distribution of a pendular liquid bridge between two unequally sized spherical particles in the presence of wetting hysteresis. Two different simplifications of the bridge geometry were considered: a toroidal and a parabolic approximation. The liquid bridge was assumed to rupture through its thinnest neck leaving liquid distributed on each sphere. Experimental measurements showed that the rupture distance was well predicted by both profile approximations by assuming that rupture occurred when the liquid–vapor interfacial area of the bridge and the postrupture droplets was equal. Both bridge profile approximations only correctly predicted the evolution of the apparent contact angle and the extent of postrupture liquid distribution when the solid–liquid interfacial area measured throughout the separation was included in the calculations. This is because during the pendular liquid bridge elongation, the three-phase contact line usually begins to slip on at least one of the spheres. The parabolic profile approximation was slightly more accurate than the toroidal one. The toroidal approximation is more difficult to use because one of the parameters passes through infinity as the bridge changes from convex to concave in shape. In some cases the toroidal approximation was also unable to generate a solution.