Kinematics of the viscous filament during the droplet breakup in air.

The dripping regime in the vicinity of the fluid droplet breakup is analyzed using the correlation between experiments and numerics. The evolutions of filament's neck and its corresponding thinning velocity are described using the logistic functions. Three flow regions are observed as the relative time decreases: (1) a monotonous increase of the neck's thinning velocity, where inertia and capillarity are balanced, (2) a transition domain characterized by the equilibrium between inertia, capillarity, and viscous forces, where the thinning velocity varies non-monotonically with the relative time and (3) the final droplet pinch-off, where velocity decreases or oscillates around a constant value. The distributions of the [Formula: see text]-coefficient (parameter related to the non-dimensional second invariant of the velocity gradient) on the filament's surface and droplet's profile characterize the kinematics at the interface. The regions dominated by extension, where pure elongation is located at [Formula: see text], are determined. One main result of this study is the confirmation that distribution of the [Formula: see text]-coefficient is a relevant parameter to analyze and to quantify the breakup process. This result has the potential of developing novel techniques and more precise procedures in determining the interfacial rheology of viscous and complex fluids.