Scaling law on formation and rupture of a dynamical liquid bridge

The formation and breakup of a pendular liquid bridge in dynamic state is investigated experimentally. The experimental setup arises from a system to measure the coefficient of restitution (COR) of a glass sphere impacting and bouncing on a wetted surface. We compare the effect of surface tension and gravity on the liquid bridge rupture by the capillary length $\kappa ^{\mathrm{-1}}$. For water and liquid 1 (50{\%} water mixed with 50{\%} glycerol), the gravity is dominant on the liquid bridge breakup. And we find that the rupture distance is in good linear trend with the non-dimensional number $G$ by the scaling law analysis. Further, for liquid 2 (25{\%} water mixed with 75{\%} glycerol) that is relatively high viscous, the linear changing of the rupture distance with the capillary number Ca is found. The relation of the rupture distance with $G$ and Ca would be helpful in understanding the complex behavior of the dynamical liquid bridge.