Formation of beads-on-a-string structures during the pinch-off of viscoelastic filaments (original) (raw)
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Formation of beads-on-a-string structures during break-up of viscoelastic filaments
Nature Physics, 2010
Breakup of viscoelastic filaments is pervasive in both nature and technology. If a filament is formed by placing a drop of saliva between a thumb and forefinger and is stretched, the filament's morphology close to breakup corresponds to beads of several sizes interconnected by slender threads. Although there is general agreement that formation of such beads-on-a-string (BOAS) structures only occurs for viscoelastic fluids, the underlying physics remains unclear and controversial. The physics leading to the formation of BOAS structures is probed by numerical simulation. Computations reveal that viscoelasticity alone does not give rise to a small, satellite bead between two much larger main beads but that inertia is required for its formation. Viscoelasticity, however, enhances the growth of the bead and delays pinch-off, which leads to a relatively long-lived beaded structure. We also show for the first time theoretically that yet smaller, sub-satellite beads can also form as seen in experiments.
The beads-on-string structure of viscoelastic threads
Journal of Fluid Mechanics, 2006
By adding minute concentrations of a high-molecular-weight polymer, liquid jets or bridges collapsing under the action of surface tension develop a characteristic shape of uniform threads connecting spherical fluid drops. In this paper, high-precision measurements of this beads-on-string structure are combined with a theoretical analysis of the limiting case of large polymer relaxation times and high polymer extensibilities, for which the evolution can be divided into two distinct regimes. For times smaller than the polymer relaxation time over which the beads-on-string structure develops, we give a simplified local description, which still retains the essential physics of the problem. At times much larger than the relaxation time, we show that the solution consists of exponentially thinning threads connecting almost spherical drops. Both experiment and theoretical analysis of a one-dimensional model equation reveal a self-similar structure of the corner where a thread is attached to the neighbouring drops. † Present address:
Journal of Non-newtonian Fluid Mechanics, 2009
Fundamental understanding of the formation and pinch-off of viscoelastic filaments is important in applications involving production of drops (e.g., ink-jet printing, micro-arraying, and atomization). In addition to delaying pinch-off, in some cases, viscoelasticity is known to cause the so-called beads-on-string structure, i.e., a number of small droplets interconnected by thin filaments. In a recent publication [H. Matallah, M.J. Banaai, K.S. Sujatha, M.F. Webster, J. Non-Newtonian Fluid Mech. 134 (2006) 77-104], it was shown that the simulation of an elongating filament modeled by the Phan-Thien/Tanner (PTT) equation with the Gordon-Schowalter (GS) convected derivative, which allows non-affine motion of polymer molecules in the continuum, results in the formation of the beads-on-string structure. On the other hand, such bead formation is not reported in calculations with other viscoelastic models that are also strain-hardening like the PTT model but do not have the GS convected derivative (see, e.g., [M. Yao, S.H. Spiegelberg, G.H. McKinley, J. Non-Newtonian Fluid Mech. 89 (2000) 1-43])
Droplet Detachment and Satellite Bead Formation in Viscoelastic Fluids
Physical Review Letters, 2005
The presence of a very small amount of high molecular weight polymer significantly delays the pinchoff singularity of a drop of water falling from a faucet and leads to the formation of a long-lived cylindrical filament. In this Letter, we present experiments, numerical simulations, and theory which examines the pinch-off process in the presence of polymers. The numerical simulations are found to be in good agreement with experiment. As a test case, we establish the conditions under which a small bead remains on the filament; we find that the presence of a bead is due to the asymmetry induced by the selfsimilar pinch off of the droplet.
2005
The dynamics of elastocapillary thinning in high molecular weight polymer solutions are reexamined using high-speed digital video microscopy. At long times, the evolution of the viscoelastic thread deviates from self-similar exponential decay and the 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 the ligaments. This iterated process results in the development of multiple generations of beads in agreement with the predictions of Chang, Demekin, and Kalaidin ͓"Iterated stretching of viscoelastic jets," Phys. Fluids 11, 1717 ͑1999͔͒ although experiments yield a different recursion relation between successive generations. At long times, finite molecular extensibility truncates the iterated instability and axial translation of the bead arrays along the interconnecting threads leads to a progressive coalescence before the rupture of the filament.
Journal of Non-Newtonian Fluid Mechanics, 2006
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] 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 capillarydriven thinning in the cylindrical ligaments between beads.
Physics of Fluids, 2005
The dynamics of elastocapillary thinning in high molecular weight polymer solutions are reexamined using high-speed digital video microscopy. At long times, the evolution of the viscoelastic thread deviates from self-similar exponential decay and the 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 the ligaments. This iterated process results in the development of multiple generations of beads in agreement with the predictions of Chang, Demekin, and Kalaidin ͓"Iterated stretching of viscoelastic jets," Phys. Fluids 11, 1717 ͑1999͔͒ although experiments yield a different recursion relation between successive generations. At long times, finite molecular extensibility truncates the iterated instability and axial translation of the bead arrays along the interconnecting threads leads to a progressive coalescence before the rupture of the filament.
Dynamics of viscoelastic liquid filaments: Low capillary number flows
Journal of Non-newtonian Fluid Mechanics, 2007
Many applications of viscoelastic free surface flows requiring formation of drops from small nozzles, e.g., ink-jet printing, micro-arraying, and atomization, involve predominantly extensional deformations of liquid filaments. The capillary number, which represents the ratio of viscous to surface tension forces, is small in such processes when drops of water-like liquids are formed. The dynamics of extensional deformations of viscoelastic liquids that are weakly strain hardening, i.e., liquids for which the growth in the extensional viscosity is small and bounded, are here modeled by the Giesekus, FENE-P, and FENE-CR constitutive relations and studied at low capillary numbers using full 2D numerical computations. A new computational algorithm using the general conformation tensor based constitutive equation [M. Pasquali, L.E. Scriven, Theoretical modeling of microstructured liquids: a simple thermodynamic approach, J. Non-Newtonian Fluid Mech. 120 (2004) 101–135] to compute the time dependent viscoelastic free surface flows is presented. DEVSS-TG/SUPG mixed finite element method [M. Pasquali, L.E. Scriven, Free surface flows of polymer solutions with models based on conformation tensor, J. Non-Newtonian Fluid Mech. 108 (2002) 363–409] is used for the spatial discretization and a fully implicit second-order predictor–corrector scheme is used for the time integration. Inertia, capillarity, and viscoelasticity are incorporated in the computations and the free surface shapes are computed along with all the other field variables in a fully coupled way. Among the three models, Giesekus filaments show the most drastic thinning in the low capillary number regime. The dependence of the transient Trouton ratio on the capillary number in the Giesekus model is demonstrated. The elastic unloading near the end plates is investigated using both kinematic [M. Yao, G.H. McKinley, B. Debbaut, Extensional deformation, stress relaxation and necking failure of viscoelastic filaments, J. Non-Newtonian Fluid Mech. 79 (1998) 469–501] and energy analyses. The magnitude of elastic unloading, which increases with growing elasticity, is shown to be the largest for Giesekus filaments, thereby suggesting that necking and elastic unloading are related.
Dynamics of bead formation, filament thinning and breakup in weakly viscoelastic jets
Journal of Fluid Mechanics, 2010
The spatiotemporal evolution of a viscoelastic jet depends on the relative magnitude of capillary, viscous, inertial and elastic stresses. The interplay of capillary and elastic stresses leads to the formation of very thin and stable filaments between drops, or to 'beads-on-a-string' structure. In this paper, we show that by understanding the physical processes that control different stages of the jet evolution it is possible to extract transient extensional viscosity information even for very low viscosity and weakly elastic liquids, which is a particular challenge in using traditional rheometers. The parameter space at which a forced jet can be used as an extensional rheometer is numerically investigated by using a one-dimensional nonlinear free-surface theory for Oldroyd-B and Giesekus fluids. The results show that even when the ratio of viscous to inertio-capillary time scales (or Ohnesorge number) is as low as Oh ∼ 0.02, the temporal evolution of the jet can be used to obtain elongational properties of the liquid.