Iterated Stretching, Extensional Rheology and Formation of
Beads-on-a-String Structures in Polymer Solutions
Mónica S. N. Oliveira, Roger Yeh and Gareth H. McKinley
Hatsopoulos Microfluids Laboratory, Department of Mechanical Engineering,
Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Submitted for the Special Issue of JNNFM on Extensional Flow, June 2006
Final Version; January 20, 2006

Abstract
The transient extensional rheology and the dynamics of elastocapillary thinning in
aqueous solutions of polyethylene oxide (PEO) are studied with high-speed digital video
microscopy. At long times, the evolution of the thread radius deviates from self-similar
exponential decay and competition between elastic, capillary and inertial forces leads to
the formation of a periodic array of beads connected by axially-uniform ligaments. This
configuration is unstable and successive instabilities propagate from the necks
connecting the beads and ligaments. This iterated process results in multiple generations
of beads developing along the string in general agreement with predictions of Chang et
al. [Phys Fluids, 11, 1717 (1999)] although the experiments yield a different recursion
relation between the successive generations of beads. At long times, finite extensibility
truncates the iterated instability, and slow axial translation of the bead arrays along
the interconnecting threads leads to progressive coalescence before the ultimate rupture
of the fluid column.  Despite these dynamical complexities it is still possible to
measure the steady growth in the transient extensional viscosity by monitoring the slow
capillary-driven thinning in the cylindrical ligaments between beads.