When a mass of liquid fragments into drops, the undergoing process essentially involves the formation, thinning, and pinch-off of filaments. Technologically, production of drops has been exploited in modern applications such as ink-jet printing and more recent printing and patterning applications such as micro-arraying of genomes or proteins, printing of biological cells, and fabrication of microelectronic components (e.g., transistors) and solar cells via certain printing techniques. Most of the liquids encountered in these applications exhibit complex, viscoelastic behavior (as opposed to simple Newtonian behavior shown by, e.g., water or glycerol) due to the presence of macromolecules such as DNA or synthetic polymers in them. Among other effects, the presence of polymers is known to cause (1) a delay in the breakup of filaments [Amarouchene et al. 2001] and (2) the formation of a topology that consists of a number of droplets interconnected by thin ligaments or the so-called beads-on-a-string structure during filament pinch-off [Goldin et al. 1969]. Thus, a clear understanding of the formation and pinch-off of viscoelastic filaments is critical in the analysis and better design of these processes. In addition, the dynamics in the region close to where pinch-off occurs is known typically to exhibit behaviors rich in physics such as universality and self-similarity [Eggers 1993].

Most studies to date have used the 1-D long-wavelength (or slender jet) approximation of the flow equations to probe the self-similar dynamics of thinning viscoelastic filaments. This approximation is clearly invalid in regions where slenderness is lost. A full 3-D time-dependent axisymmetric (2-D) numerical analysis of the problem is presented here. Fluid viscoelasticity is captured 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 [Chen, Notz, and Basaran 2001, 2002]. The dynamics of thinning viscoelastic filaments in the low capillary number regime is also studied. The results from this study are valuable in assessing experiments that are based on the breakup of filaments of low viscosity, water-like liquids (e.g., the filament stretching rheometry and the capillary breakup extensional rheometry). Experimentally, formation of drops of polymeric liquids is studied using drop-on-demand (DOD) ink jet dispensers at room and elevated temperatures and the potential of the DOD technology in applications such as deposition of drugs on different substrates is explored.