Linda B. Smolka

On the pinch-off of a pendant drop of viscous fluid

The pinch-off of a drop of viscous fluid is observed using high-speed digital imaging. The behavior seen by previous authors is observed here; namely, the filament that attaches the drop to the orifice evolves into a primary thread attached to a much thinner, secondary thread by a slight bulge. Here, we observe that the lengths of the primary and secondary threads are reproducible among experiments to within 3% and 10%. The secondary thread becomes unstable as evidenced by wave-like disturbances. The actual pinch-off does not occur at the point of attachment between the secondary thread and the drop. Instead, it occurs between the disturbances on the secondary thread. After the initial pinch-off, additional breaks occur between the disturbances, resulting in several secondary satellite drops with a broad distribution of sizes. The pinch-off of the thread at the orifice is similar to that at the drop with one main difference: there is no distinct secondary thread. Instead, the primary thread necks down mon...

The motion of a falling liquid filament

When a liquid drop falls from a fluid source with a slow flow rate, it remains attached to the source by an elongating liquid filament until the filament pinches off. For many fluids, this pinch-off occurs first near the end of the filament, where the filament joins to the liquid drop. For other fluids, the filament pinches off at one or more interior points. In this paper, we study the motion of this filament, and we make two points. First, the flow in this filament is not that of a uniform jet. Instead, we show experimentally that a different solution of the Navier–Stokes equations describes the motion of this filament before it pinches off. Second, we propose a criterion for the location of the first pinch-off. In particular, we analyze the linearized stability of the exact solution, both for an inviscid fluid and for a very viscous fluid. Our criterion for pinch-off is based on this stability analysis. It correctly predicts whether a given filament pinches off first near its ends or at points within i...

Drop pinch-off and filament dynamics of wormlike micellar fluids

Observations are presented of several novel phenomena involved in the dynamics of a pendant drop of viscoelastic micellar fluid falling through air. Generally, when a drop falls a filament forms connecting it to the orifice; the filament eventually breaks due to an instability. The filament dynamics and instabilities reported here are very different from the standard Newtonian and non-Newtonian cases. At low surfactant concentration, the cylindrical filament necks down and pinches off rapidly (∼10 ms) at one location along the filament. After pinch-off, the free filament ends retract and no satellite drops are produced. At higher concentrations, the pinch-off also occurs along the filament, but in a more gradual process (∼1 s). Furthermore, the free filament ends do not fully retract, instead retaining some of their deformation. The falling drop is also observed to slow or even stop (stall) before pinch-off, indicating that sufficient elastic stress has built up to balance its weight. We investigate this stall by generalizing Keiller’s simple model for filament motion [J. Non-Newtonian Fluid Mech. 42 (1992) 37], using instead the FENE-CR constitutive equation. Numerical simulations of this model indicate that stall occurs in the range of low solvent viscosity, high elasticity, and high molecular weight. At the highest concentrations, we observe a surface “blistering” instability along the filament long before pinch-off occurs.

Dynamics of free surface perturbations along an annular viscous film

It is known that the free surface of an axisymmetric viscous film flowing down the outside of a thin vertical fiber under the influence of gravity becomes unstable to interfacial perturbations. We present an experimental study using fluids with different densities, surface tensions, and viscosities to investigate the growth and dynamics of these interfacial perturbations and to test the assumptions made by previous authors. We find that the initial perturbation growth is exponential, followed by a slower phase as the amplitude and wavelength saturate in size. Measurements of the perturbation growth for experiments conducted at low and moderate Reynolds numbers are compared to theoretical predictions developed from linear stability theory. Excellent agreement is found between predictions from a long-wave Stokes flow model [Craster and Matar, J. Fluid Mech. 553, 85 (2006)] and data, while fair to excellent agreement (depending on fiber size) is found between predictions from a moderate-Reynolds-number model [Sisoev, Chem. Eng. Sci. 61, 7279 (2006)] and data. Furthermore, we find that a known transition in the longer-time perturbation dynamics from unsteady to steady behavior at a critical flow rate Q(c) is correlated with a transition in the rate at which perturbations naturally form along the fiber. For Q<Q(c) (steady case), the rate of perturbation formation is constant. As a result, the position along the fiber where perturbations form is nearly fixed, and the spacing between consecutive perturbations remains constant as they travel 2 m down the fiber. For Q>Q(c) (unsteady case), the rate of perturbation formation is modulated. As a result, the position along the fiber where perturbations form oscillates irregularly, and the initial speed and spacing between perturbations varies, resulting in the coalescence of neighboring perturbations further down the fiber.

Exact solution for the extensional flow of a viscoelastic filament

We solve the free boundary problem for the dynamics of a cylindrical, axisymmetric viscoelastic filament stretching in a gravity-driven extensional flow for the Upper Convected Maxwell and Oldroyd-B constitutive models. Assuming the axial stress in the filament has a spatial dependence provides the simplest coupling of viscoelastic effects to the motion of the filament, and yields a closed system of ODEs with an exact solution for the stretch rate and filament thickness satisfied by both constitutive models. This viscoelastic solution, which is a generalization of the exact solution for Newtonian filaments, converges to the Newtonian power-law scaling as

Fingering instability down the outside of a vertical cylinder

t \rightarrow \infty

On the planar extensional motion of an inertially driven liquid sheet

. Based on the exact solution, we identify two regimes of dynamical behavior called the weakly- and strongly-viscoelastic limits. We compare the viscoelastic solution to measurements of the thinning filament that forms behind a falling drop for several semi-dilute (strongly-viscoelastic) polymer solutions. We find the exact solution correctly predicts the time-dependence of the filament diameter in all of the experiments. As

Dynamics of a thermally driven film climbing the outside of a vertical cylinder

t \rightarrow \infty

Biaxial extensional motion of an inertially driven radially expanding liquid sheet

, observations of the filament thickness follow the Newtonian scaling

Charge screening effects on filament dynamics in xanthan gum solutions

1/\sqrt{t}