Iterated stretching and multiple beads-on-a-string phenomena in dilute solutions of flexible macromolecules (original) (raw)
Related papers
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.
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.
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.
Formation of beads-on-a-string structures during the pinch-off of viscoelastic filaments
2009
Breakup of liquid filaments is omnipresent in nature and technology. When a filament formed by placing a drop of syrup between a thumb and a forefinger is stretched by pulling apart the two fingers, it resembles a thinning cylinder. If the same experiment is repeated with saliva, the filament's morphology close to pinch-off resembles that of beads of several sizes interconnected by slender threads. Although there is general agreement that formation of such beads-on-a-string (BOAS) morphology only occurs for viscoelastic fluids, the mechanism behind this phenomenon remains unclear and controversial. The physics of formation of BOAS structures is probed here by simulation which reveals that viscoelasticity alone does not give rise to a small, satellite bead between two much larger main drops (beads) but that inertia is required for its formation. Viscoelasticity, however, enhances the growth of the satellite bead and delays pinch-off, which leads to a relatively long-lived, stable beaded filament. The new simulations also show the formation of second-generation sub-satellite beads in certain cases, as observed experimentally but not, heretofore, predicted theoretically.
Response of Flexible Polymers to a Sudden Elongational Flow
Science, 1998
Individual polymers at thermal equilibrium were exposed to an elongational flow producing a high strain rate, and their dynamics were recorded with video fluorescence microscopy. The flow was turned on suddenly so that the entire evolution of molecular conformation could be observed without initial perturbations. The rate of stretching of individual molecules is highly variable and depends on the molecular conformation that develops during stretching. This variability is due to a dependence of the dynamics on the initial, random equilibrium conformation of the polymer coil. The increasing appearance at high strain rates of slowly unraveling hairpin folds is an example of nonergodic dynamics, which can occur when a statistical mechanical system is subjected to nonadiabatic, or “sudden,” external forces.
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:
Kinematics of filament stretching in dilute and concentrated polymer solutions
2001
The development of filament stretching extensional rheometers over the past decade has enabled the systematic measurement of the transient extensional stress growth in dilute and semi-dilute polymer solutions. The strain-hardening in the extensional viscosity of dilute solutions overwhelms the perturbative effects of capillarity, inertia & gravity and the kinematics of the extensional deformation become increasingly homogeneous at large strains. This permits the development of a robust open-loop control algorithm for rapidly realizing a deformation with constant stretch history that is desired for extensional rheometry. For entangled fluids such as concentrated solutions and melts the situation is less well defined since the material functions are governed by the molecular weight between entanglements, and the fluids therefore show much less pronounced strain-hardening in transient elongation. We use experiments with semi-dilute/entangled and concentrated/entangled monodisperse polystyrene solutions coupled with time-dependent numerical computations using nonlinear viscoelastic constitutive equations such as the Giesekus model in order to show that an open-loop control strategy is still viable for such fluids. Multiple iterations using a successive substitution may be necessary, however, in order to obtain the true transient extensional viscosity material function. At large strains and high extension rates the extension of fluid filaments in both dilute and concentrated polymer solutions is limited by the onset of purely elastic instabilities which result in 'necking' or 'peeling' of the elongating column. The mode of instability is demonstrated to be a sensitive function of the magnitude of the strain-hardening in the fluid sample. In entangled solutions of linear polymers the observed transition from necking instability to peeling instability observed at high strain rates (of order of the reciprocal of the Rouse time for the fluid)
What controls filament thinning in uniaxial extension?
Korea-Australia Rheology Journal, 2019
Breakup of fluid threads is omnipresent in nature and highly relevant for technical processes such as atomization, printing, coating, or spinning. We discuss how to control the filament lifetime of shear-thinning, viscoelastic fluids during uniaxial extension without affecting their shear viscosity. Two commercial acrylic thickeners differing with respect to the co-polymerized hydrophobic monomers, and hence different hydrophobic intra-and intermolecular association, are mixed to obtain aqueous solutions with similar shear viscosity. The elongational relaxation time as determined by capillary breakup extensional rheometry, however, varies by almost two orders of magnitude. Filament lifetime of these solutions can be varied upon adding non-Brownian, plate-shaped particles, again without affecting shear viscosity. A trace amount of particles increases elongational relaxation time by about a factor of four. Car bodies are usually coated using highspeed rotary bell atomizers guaranteeing high transfer efficiency and high-quality appearance. We use the solutions and suspensions described above to investigate the effect of extensional viscosity on ligament formation at the bell edge as a decisive intermediate step prior to droplet formation. High-speed imaging reveals a logarithmic scaling of ligament length with extensional relaxation time for pure thickener solutions. In contrast, ligament length monotonically decreases with increasing particle concentration, i.e. extensional viscosity. Plate-shaped particles obviously act as defects promoting ligament breakup. Extended filament lifetimes are commonly observed during atomization and spraying as a consequence of fluid viscoelasticity. On the other hand, low viscosity fluid threads rupture quickly. Here, we demonstrate that a unique banding instability during extension of a low viscosity surfactant solution with no measurable elasticity leads to extremely long filament lifetimes and to the formation of remarkably long threads. Combining filament stretching and particle image velocimetry we found an unexpected heterogeneous, banded flow in opposing directions. This phenomenon is not limited to surfactant solutions but can also occur in biopolymer solutions, thus broadening the view on instabilities in complex elongational flows.
Iterated stretching of viscoelastic jets
Physics of Fluids, 1999
We examine, with asymptotic analysis and numerical simulation, the iterated stretching dynamics of FENE and Oldroyd-B jets of initial radius r 0 , shear viscosity , Weissenberg number We, retardation number S, and capillary number Ca. The usual Rayleigh instability stretches the local uniaxial extensional flow region near a minimum in jet radius into a primary filament of radius ͓Ca(1ϪS)/We͔ 1/2 r 0 between two beads. The strain-rate within the filament remains constant while its radius ͑elastic stress͒ decreases ͑increases͒ exponentially in time with a long elastic relaxation time 3We(r 0 2 /). Instabilities convected from the bead relieve the tension at the necks during this slow elastic drainage and trigger a filament recoil. Secondary filaments then form at the necks from the resulting stretching. This iterated stretching is predicted to occur successively to generate high-generation filaments of radius r n , (r n /r 0 )ϭ&(r nϪ1 /r 0 ) 3/2 until finite-extensibility effects set in.