Fragmentation of stretched liquid ligaments

The dynamics and fragmentation of stretched liquid ligaments is investigated. The ligaments are produced by the withdrawal of a tube initially dipping at a free surface. Time resolved high speed motion experiments reveal two different elongation behaviors, depending on the nondimensional number ε̇tσ, ratio of the extension rate ε̇ to the capillary contraction rate 1/tσ, with tσ the capillary time based on the tube diameter. For slow extensions (small ε̇tσ) the liquid bridge linking the tube to the reservoir contracts above a critical elevation, eventually following a self-similar contraction before break-up. For fast extensions (large ε̇tσ) the bridge takes the form of a cylindrical ligament, stabilized by the stretching motion. Whatever the elongation rate is, the ligament detaches from the surface at a time of order tσ after the beginning of the extension. If only one small droplet is produced with a slowly stretched bridge, a set of droplets with distributed sizes is obtained from the break-up of the ligament submitted to a fast extension. We discover that an aggregative process comes into play between the blobs constitutive of the ligament as it fragments. The outcoming Gamma distribution describes well the observed broad drop size distributions.