Role of Dimensionality and Axisymmetry in Fluid Pinch-Off and Coalescence

We present data on the pinch-off and coalescence of thin liquid alkane lenses floating on water. Pinch-off in quasi-2D lenses is distinctly different from pinch-off in axisymmetric 3D drops and involves a cascade of satellite droplets which extends to micron length scales. In contrast, coalescence of lenses is qualitatively similar to coalescence of 3D drops. Coalescence is predicted to involve entrainment of the exterior fluid as the droplets merge. This reentrant folding is obscured in 3D droplets but is clearly visible in coalescence of thin lenses.

Figure 1

(a) Breakup of a 3D decane droplet immersed in water just after pinch-off. Both the cone-shaped structure and the dark region at the bottom are decane. The neck has a well-defined angle and rounded tip characteristic of inviscid pinch-off [24]. (b) Breakup of a quasi-2D decane lens on the surface of water just after pinch-off at the same magnification as (a). A cascade of pinch-off events creates multiple satellite droplets in a fractal-like structure. The bottom of the image is the large lens shown in the right-hand edge of the images in Fig. 2.

Figure 2

Video frames of the breakup of a decane lens illuminated from below. Magnification is indicated by the bars. The vertical sequence shows the central region of the filament as it undergoes a cascade of pinches. The time interval between frames is $748\mu \mathrm{s}$. The high magnification image just below the sequence shows just the right half of this filament immediately after breakup, which displays a complex structure of the remaining satellite lenses. Multiple satellite lenses are formed in a range of sizes which extends to below our optical resolution of $2.2\mu \mathrm{m}$ per pixel.

Figure 3

(a) Coalescence of two dodecane lenses. The curvature of a dodecane lens is large enough to scatter the light and appear dark. At the moment of connection, a light spot appears, indicating that the curvature is flattened as the two lenses merge together. The time interval between frames is $748\mu \mathrm{s}$. (b) Log-log plot of the minimum radius ($r_{\min }$) of the connecting necks between two dodecane lenses during coalescence versus the time elapsed from the initial connection ($\tau$). The change in slope signifies a transition between inertial-capillary ($r_{\min }\propto {\tau }^{1/2}$) and viscous-capillary scaling ($r_{\min }\propto \tau$), as indicated by the dashed and solid lines, respectively. The crossover length $l_c$ is indicated by the arrow. Note that the coefficients of the scaling forms are of the order of 1.

Figure 4

High magnification images of the coalescence of two octane lenses. The dark line is the three-phase air-water-octane contact line. The initial coalescence event triggers an instability which results in multiple holes that become trapped in the film and then eventually disappear when the alkane closes around them. The time interval between frames is $180\mu \mathrm{s}$.