On the motion of Newtonian and non-Newtonian liquid filaments: Stretching, beading, blistering, pinching

The motion and stability of a liquid filament drawn out behind a falling drop is examined experimentally and mathematically for Newtonian and non-Newtonian fluids. We confirm experimentally that an exact solution for the interfacial motion of an infinite Newtonian filament captures the thinning of the filament in experiments with several fluids. We also show experimentally that a linear stability analysis of this solution correctly predicts whether the filament end-pinches or internally-pinches, creating either one or several satellite drops. We derive an exact solution for a purely extensional cylindrical filament of non-Newtonian fluid that satisfies both the Upper Convected Maxwell and Oldroyd-B constitutive laws. The resulting prediction of decreasing filament thickness agrees with our experimental measurements for dilute polymer solutions. In the limit t → ∞, the exact solution approaches that for a Newtonian fluid. In experiments with a polyelectrolyte polymer (xanthan gum) solution, the drop length sensitively depends on the ionic strength of the solvent environment due to charge screening effects. We also study the “beadon-string” phenomenon, in which a nascent disturbance grows to finite size along a filament. In experiments with an aqueous polymer solution the perturbation grows logarithmically, and may saturate in size to a nearly spherical shape. Numerical simulations of a simple 1-D model for the bead predicts the logarithmic growth, but fail to capture saturation. Finally, in experiments with surfactant solutions composed of wormlike micelles, with low concentrations, the drop pinches-off in one location along the filament, and the free filament ends contract toward the orifice or drop. For higher concentrations, this free filament does not fully retract, instead it retains some of its deformation. The drop may also stall in its downward motion, such that elasticity balances the weight of the drop. For still higher concentration surfactant solutions a new surface instability develops along the filament, which we term surface blistering. We simulate a simple 1-D model that predicts the drop stall for fluids with low solvent viscosity, high elasticity and high molecular weight. The surface blistering and drop stall may be evidence of a transition from fluid to gel-like behavior in the filament.