Iterated stretching and multiple beads-on-a-string phenomena in dilute solutions of flexible macromolecules

Gareth H. McKinley
Hatsopoulos Microfluids Laboratory
Department of Mechanical Engineering, M.I.T., Cambridge MA 02139, USA

It has been known for at least 40 years that the dynamics of capillary thinning and breakup of polymeric jets and threads are substantially different from the equivalent processes in Newtonian fluids. The capillary necking induced by surface tension results in a strong uniaxial stretching flow in the thread which leads to large molecular elongation and inhibits the finite time singularity associated with breakup in a Newtonian fluid jet. As a result of the absence of external forcing the dynamics of the necking process are often self-similar and observations of this 'self-thinning' can be used to extract the transient extensional viscosity of the material. The large viscoelastic stresses resulting from this stretching can also lead to iterated dynamical processes that result in self-similar spatial structures such as a 'beads on a string' morphology in which spherical fluid droplets are interconnected by long thin fluid ligaments. Understanding the distribution of the droplets resulting from the dynamics of this process is important in numerous commercial applications including jet breakup, fertilizer spraying, roll-coating, electrospinning, and inkjet printing. In the present work, the spatio-temporal dynamics of elastocapillary thinning and jet breakup in high molecular weight flexible polymer solutions are re-examined using high-speed digital video microscopy. At long times, the evolution of the viscoelastic thread deviates from the self-similar exponential decay and competition of elastic, capillary and inertial forces leads to the formation of a periodic array of beads connected by axially-uniform ligaments. This configuration is itself 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)]. However, the experiments yield a different recursion relation between successive generations of beads from that predicted theoretically. At long times, finite extensibility truncates the iterated instability and axial translation of the of the bead arrays along the interconnecting threads leads to progressive coalescence before the ultimate rupture of the fluid column.