Extremes of the pinch-off location and time in a liquid column by an accelerating solid sphere

Abstract

When a solid body rises from a bath, a liquid column is formed and stretched until pinch-off occurs at different locations and times. In the present paper, we study the temporal and spatial evolution of a less viscous liquid column extracted by an accelerating sphere from a bath. At high acceleration, the observed liquid column has the shape of an up-pointing cone, which implies that the column near the sphere is stretched so quickly that the liquid cannot keep up with it. This causes the liquid column to pinch off at the upper location. At low accelerations, a liquid column pinches off at a lower location near the free surface. The shift in the pinch-off location is explained by the axial velocity-gradient profile in the liquid column. The numerical results show that the gradient of the axial velocity near the sphere increases when the solid sphere has a higher acceleration. As a result, at high accelerations, the axial velocity gradient is responsible for the necking and pinching off at the upper location of the liquid column. At low sphere accelerations, the column pinches off at the lower location by the strong Laplace pressure due to the higher gradient of the interfacial curvature between the column and the bath. Next the pinch-off time is observed to decrease as the acceleration increases regardless of the pinch-off location. We use a linear stability analysis to predict the pinch-off time as the inverse of the growth rate in the dispersion relation.