Dynamics of Contracting Asymmetric Viscoelastic Filaments

In ink-jet printing and atomization, slender filaments are routinely formed.~~Such filaments either contract to form a single drop or breakup into multiple drops, e.g. by end pinching. Beginning with papers by Schulkes (1996) and Notz {\&} Basaran (2004), past studies have focused exclusively on the contraction dynamics of Newtonian filaments.~~Also in these studies, initial filament shapes are taken to be long cylinders terminated by two identical spherical caps (symmetric filaments).~~In emerging applications, e.g. ink-jet printing of complex fluids, the filaments are viscoelastic (VE) fluids.~~Moreover, older experiments by Notz et al. (2001) and more recent ones by Castrej\'{o}n-Pita et al. (2012) show that initial filament shapes resemble long, tapered cylinders terminated by hemispherical caps of unequal radii (asymmetric filaments).~~Therefore, we analyze the contraction dynamics of both asymmetric and symmetric filaments of VE fluids using the Giesekus model.~~Rather than solving the full set of equations governing the problem, we take advantage of filament slenderness and solve a much simpler set of 1D equations (Eggers, 1997).~~We then use a finite element method with Streamline Upwind/Petrov Galerkin (SUPG) formulation (Brooks {\&} Hughes, 1982) to solve the reduced equations.