Contraction of a filament of an incompressible Newtonian liquid in a passive ambient fluid is studied computationally to provide insights into the dynamics of satellite drops created during drop formation. This free boundary problem, which is composed of the Navier–Stokes system and the associated initial and boundary conditions that govern the evolution in time of the filament shape and the velocity and pressure fields within it, is solved by the method of lines incorporating the finite element method for spatial discretization. The finite element algorithm developed here utilizes an adaptive elliptic mesh generation technique that is capable of tracking the dynamics of the filament up to the incipience of pinch-off without the use of remeshing. The correctness of the algorithm is verified by demonstrating that its predictions accord with (a) previously published results of Basaran (1992) on the analysis of finite-amplitude oscillations of viscous drops, (b) simulations of the dynamics of contracting filaments carried out with the well-benchmarked algorithm of Wilkes et al. (1999), and (c) scaling laws governing interface rupture and transitions that can occur from one scaling law to another as pinch-off is approached. In dimensionless form, just two parameters govern the problem: the dimensionless half-length $L_o$ and the Ohnesorge number $Oh$ which measures the relative importance of viscous force to capillary force. Regions of the parameter space are identified where filaments (a) contract to a sphere without breaking into multiple droplets, (b) break via the so-called endpinching mechanism where daughter drops pinch-off from the ends of the main filament, and (c) break after undergoing a series of complex oscillations. Predictions made with the new algorithm are also compared to those made with a model based on the slender-jet approximation. A region of the parameter space is found where the slender-jet approximation fares poorly, and its cause is elucidated by examination of the vorticity dynamics and flow fields within contracting filaments.

Pinch-off and scaling during drop formation are studied using high-accuracy computation and ultrafast, high-resolution imaging. The interface of a water drop (viscosity mu is approximately 1 cP) is shown to overturn prior to breakup for the first time in experiments, well before the dynamics transitions from the potential flow (PF) to the inertial-viscous (IV) regime. A drop of 83% glycerol-water solution (mu is approximately 85 cP) is shown to exhibit a transition from the PF to the IV regime both computationally and experimentally. The computed value of the minimum neck radius in the latter case follows Eggers's universal solution until it becomes unstable.

During drop formation from a tube, a thin liquid thread—the precursor to satellites—connects an about-to-form primary drop to the remainder of the liquid hanging from the tube at the incipience of breakup. Whether the thread, once it detaches from the primary and pendant drops, evolves into a sphere or breaks into several subsatellites has heretofore been inadequately explored due to experimental and theoretical difficulties. These challenges are resolved here with an ultrafast digital imaging system and a novel computational algorithm. New findings range from the discovery of unexpected dynamics to the first demonstration of the transition from one scaling law governing interface rupture to another.

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