Pinch-off of liquid bridge during droplet coalescence under constrained condition

In this study, we perform an experimental investigation on the dynamical behaviors of a liquid bridge formed during droplet coalescence. Notably, the two droplets are constrained respectively by two vertically aligned needles. Of particular interest is the pinch-off of the liquid bridge under this constrained condition. We observe three typical behaviors of the liquid bridge: (1) reaching a stable shape after damped oscillations (regime I); (2) pinching off at both sides in the first necking stage with the largest oscillation amplitude (regime II); and (3) pinching off at only the upper side after once or twice necking (regime III). To indicate the condition when the pinch-off of the liquid bridge may occur, we develop a phase diagram based on the radius ratio of the droplet to the needle Rd/Rn and the Bond number Bo, which respectively characterizes the relative importance of surface tension to the constraint force from needles and that of gravity to surface tension. In general, the dynamical behavior of the liquid bridge transitions from regime II to regime I with Rd/Rn decreasing, and the critical value for this transition is 1.6. This transition indicates that the constraint force keeps the liquid bridge stable while the surface tension promotes its instability. Surprisingly, once the Bond number is sufficiently high (e.g., Bo > 0.05), regime III (i.e., pinch-off at only the upper side) is observed when Rd/Rn becomes around the regime II to I transition (i.e., Rd/Rn = 1.6). It is because the effect of gravity becomes predominant over the surface tension and the constrained force from needles. Moreover, we analyze the pinch-off characteristics of the liquid bridge lying in regimes II and III, including its pinch-off time (i.e., the time interval from the formation and pinch-off of the liquid bridge) and its neck shape at the instant of pinching off.