On the pinch-off of a pendant drop of viscous fluid

Abstract

The pinch-off of a drop of viscous fluid is observed using high-speed digital imaging. The behavior seen by previous authors is observed here; namely, the filament that attaches the drop to the orifice evolves into a primary thread attached to a much thinner, secondary thread by a slight bulge. Here, we observe that the lengths of the primary and secondary threads are reproducible among experiments to within 3% and 10%. The secondary thread becomes unstable as evidenced by wave-like disturbances. The actual pinch-off does not occur at the point of attachment between the secondary thread and the drop. Instead, it occurs between the disturbances on the secondary thread. After the initial pinch-off, additional breaks occur between the disturbances, resulting in several secondary satellite drops with a broad distribution of sizes. The pinch-off of the thread at the orifice is similar to that at the drop with one main difference: there is no distinct secondary thread. Instead, the primary thread necks down monotonically until wave-like disturbances form, resulting in pinch-off at multiple sites in between. The speed of the tips of the retreating, secondary threads after pinch-off are reported and discussed in the context of various scaling laws.