Dynamics of contracting filaments

The contraction of liquid filaments plays a central role in applications as diverse as inkjet printing and atomization where the formation of monosized primary drops is desirable, but that of smaller satellite droplets is typically undesirable. In order to avoid polydisperse drop sizes and/or minimize the deleterious consequences of satellite droplet production, contracting or retracting filaments formed during drop pinch-off and liquid atomization should either contract to spheres without further breakup or break into equally sized drops. Therefore, given the importance of understanding the fate of contracting filaments, high-accuracy numerical simulations are used to analyze the retraction of Newtonian liquid filaments in a passive outer fluid. Previously, Notz and Basaran [Notz and Basaran, J. Fluid Mech. 512, 223 (2004)] provided a comprehensive description of the dynamics of low-viscosity filaments and subsequent studies have helped to advance our understanding of the response of moderate- to high-viscosity filaments. However, as it is shown here, combining the findings of all of these separate works does not provide a complete picture of the rich physics of filament contraction. In this work, a comprehensive approach is adopted to further refine and expand upon earlier works to provide a complete phase diagram of filament retraction dynamics by considering the entire possible range of fluid properties and initial aspect ratios for filaments undergoing contraction. In doing so, a different mode of breakup, herein referred to as capillary wave breakup, is discovered and shown to be the dominant mode of pinch-off for moderately viscous filaments. The mechanism for the breakup of filaments of moderately viscous fluids is detailed along with a thorough investigation of the already established modes of breakup for nearly inviscid and highly viscous filaments.