(365a) Formation of Beads-on-a-String during Pinch-off of Viscoelastic Filaments

How liquid filaments form, thin, and pinch-off is important in diverse applications that involve the production of drops, e.g., ink-jet printing, micro-arraying of DNA or proteins, and fabrication of microelectronic devices such as transistors via certain printing techniques. Unlike simple Newtonian fluids like water or glycerol, liquids used in these applications exhibit complex rheological (viscoelastic) behavior due to the presence of macromolecules such as DNA (e.g., in DNA micro-arraying) or synthetic polymers (e.g., in the fabrication of transistors). The presence of polymers, even in small quantities, is known to affect the dynamics of filament breakup significantly by delaying the time of pinch-off [Amarouchene et al. 2001], and, in some cases, causing the formation of a topology consisting of a sequence of droplets interconnected by small ligaments?the beads-on-a-string (BOAS) structure [Goldin et al. 1969, Oliveira and McKinley 2005, Sattler et al. 2008]. While the former effect influences the stability of thin connecting ligaments during drop formation, the latter effect may give rise to the production of undesirable satellite drops that can cause, for example, smudging in printing applications and loss of accuracy in arraying. Although there have been several experimental studies of the BOAS phenomenon, theoretical understanding of the problem is still evolving. Earlier numerical studies that focus on the formation of BOAS structure use the 1-D long-wave approximation of the flow equations [Chang et al. 1999, Li and Fontelos 2003]. This approximation does not capture accurately the physical phenomena which become important at short wavelengths. A full 3-D time-dependent axisymmetric (2-D) numerical method is used here to analyze the various physical forces that control the formation and evolution of the BOAS structure. The fluid viscoelasticity is modeled using a conformation tensor approach [Pasquali and Scriven 2002] and the governing equations are solved using a fully-coupled finite element method that has been well benchmarked against experiments in simulating the dripping of drops of Newtonian fluids [Chen, Notz, and Basaran 2001, 2002].