Breakup of Liquid Filaments

Whether a thin filament of liquid separates into two or more droplets or eventually condenses lengthwise to form a single larger drop depends on the liquid’s density, viscosity, and surface tension and on the initial dimensions of the filament. Surface tension drives two competing processes, pinching-off and shortening, and the relative time scales of these, controlled by the balance between capillary and viscous forces, determine the final outcome. Here we provide experimental evidence for the conditions under which a liquid filament will break up into drops, in terms of a wide range of two dimensionless quantities: the aspect ratio of the filament and the Ohnesorge number. Filaments which do not break up into multiple droplets demand a high liquid viscosity or a small aspect ratio.

Figure 1

Geometry of a free cylindrical liquid filament with spherical end caps as assumed in the models of Schulkes [10] and Notz and Basaran [11].

Figure 2

Apparatus with a nozzle of variable diameter used to generate liquid jets.

Figure 3

Examples of drive voltage waveforms (upper traces) and resulting pressure waveforms (lower traces) used to produce symmetrical filaments for: (a) $\mathrm{Oh}=0.01$ and $L_0=2.9$; (b) $\mathrm{Oh}=0.04$ and $L_0=9.0$; (c) $\mathrm{Oh}=0.18$ and $L_0=29.2$; (d) $\mathrm{Oh}=1.01$ and $L_0=59.0$.

Figure 4

Images of filaments generated by the drive waveforms shown in Fig. 3, together with their shapes after the times shown, for the following liquid viscosities and filament half-lengths: (a) $\mu =2\mathrm{mPa}\mathrm{s}$ and $R_0=0.95\mathrm{mm}$; (b) $\mu =5\mathrm{mPa}\mathrm{s}$ and $R_0=0.19\mathrm{mm}$; (c) $\mu =20\mathrm{mPa}\mathrm{s}$ and $R_0=0.22\mathrm{mm}$; (d) $\mu =100\mathrm{mPa}\mathrm{s}$ and $R_0=0.13\mathrm{mm}$.

Figure 5

Results plotted in terms of Oh and $L_0$. Solid symbols represent cases where the filament broke up into two or more droplets and open symbols where the filament contracted into a single droplet. The error bars represent uncertainty associated with the measurements of filament length and diameter. The shaded area shows the predictions of the model of Notz and Basaran [11]. The hatched region represents the range of critical Oh predicted by Schulkes [10]. Stars represent the points explored by Schulkes in which breakup does not occur. The broken line corresponds to the prediction of the linear instability analysis.