On the evolution of the drop-filament corner region during the pinch-off of viscoelastic fluids

Fluid pinch-off is important in applications involving the production of drops, e.g., ink-jet printing and atomization, and in the capillary breakup extensional rheometry (CaBER). A characteristic feature of fluid pinch-off is the formation of drops that are connected to thinning threads. In the pinch-off of viscoelastic fluids, the region that connects the drops to the threads develops into a sharp corner. Recently, Clasen {\em et al}.\ [J.\ Fluid Mech.\ {\bf 556}, 283 (2006)] showed that such a corner evolves self-similarly---a result which can be exploited in estimating accurately the extensional viscosity of fluids from CaBER experiments. However, the agreement between the similarity solution derived by Clasen {\em et al}.\ and experiments is only qualitative, and it may be due to their approximation of the dynamics in the corner region by a one-dimensional analysis. The evolution of the drop-filament corner region is elucidated here using theory and both one- and two-dimensional computations. A new similarity solution is obtained which describes better the shape of the liquid-gas interface in the corner region, and the dynamics in the corner region is demonstrated to be two-dimensional.