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.Take a drop of saliva from the top of your tongue or between your cheek and gums, place it between your thumb and forefinger, and then pull your fingers slowly apart to a distance of about a centimeter. With a little practice, you will see a complex, poorly understood, and practically relevant non-Newtonian fluid dynamical process evolve before your eyes. The small thread of fluid saliva first starts to thin and drain under the action of capillarity but rather than rapidly breaking-as a thread of a Newtonian fluid like water would-it persists and evolves into a periodic pattern of beads strung together as a fluid necklace as shown in By contrast, the drop of saliva shown in Figure 1(a) has no rigid cylindrical core; yet, in our digital rheometer, it displays a BOAS morphology. Therefore, the formation of the bead necklace must have a different origin in such fluids. One key requirement for the formation of beads in whole saliva is the presence of long chains of highly extensible polymer molecules such as mucopolysaccharides 9 that impart viscoelasticity to the fluid. It is widely accepted that the large viscoelastic stresses resulting from the elongation of these macromolecules resist thinning and play the same role as the rigid core. Here we show that, though necessary, viscoelasticity alone is not sufficient for the formation of beaded structures. Moreover, weshow that the BOAS phenomenon relies on the delicate interplay of four forces: capillary, viscous, elastic, and inertial. Indeed, when any of these forces dominates the others, it can overwhelm the dynamics of bead formation.The material properties of saliva vary across the population but typical values of saliva's density ρ, zero-shear-rate viscosity η 0 , and surface tension γ (ρ ∼ 1000 kg/m 3 , η 0 ∼ 1 mPa·s, and γ ∼ 60 mN/m) 9,10 are not markedly different from those of water-a low-viscosity or nearly inviscid fluid. However, the lifetime of the thread of saliva (with an initial radius R 2 of, say, 1 mm) is markedly longer than the simple estimate obtained by ...
Inkjet printers eject drops from microscopic nozzles and deposit them on substrates. For a number of years after its initial development, inkjet printing remained a method for visualizing computer output and printing documents. Beginning in the late 1990s, a number of researchers realized that inkjet printers could be employed as robotic pipettes to create microarrays, manufacture three-dimensional parts and spherical particles, print electrical devices, and facilitate combinatorial chemistry. Although most inks are low-viscosity Newtonian fluids, liquids in new applications are complex fluids. At the same time that these new applications were emerging, the replacement of traditional photography by digital imaging and the quest for ever-faster printing speeds resulted in the development of novel printing methods. Whereas most previous reviews of the field have focused on evaluations of well-known printing methods, this review instead presents a critical analysis from a fluid mechanics perspective of the recent developments in nonstandard printing techniques and the increasingly widespread use of nonstandard inks of complex fluids.
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 2-D numerical computations. A new computational algorithm using the general conformation tensor based constitutive equation [J. Non-Newtonian Fluid Mech., 120:101-135, 2004.] to compute the time dependent viscoelastic free surface flows is presented. DEVSS-TG/SUPG mixed finite element method [J. Non-Newtonian Fluid Mech., 108:363-409, 2002.] 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 [J. Non-Newtonian Fluid Mech., 79:469-501, 1998.] 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.
A characteristic feature of pinch-off of fluid threads is the formation of drops connected to thinning filaments. This phenomenon is encountered in a number of widely used applications requiring the production of drops such as electronics microfabrication via inkjet printing, spray coating/drying, and microarraying. In pinch-off of viscoelastic fluid threads, the region that connects the drops to the filaments develops into a sharp corner. Recently, Clasen et al. [J. Fluid Mech. 556, 283–308 (2006)]10.1017/S0022112006009633 showed that such a corner evolves self-similarly. They, however, neglected the capillary pressure in the drop. A modified similarity solution is presented here that incorporates the drop capillary-pressure term, and transient simulations of corner region profiles are shown to converge onto the new similarity solution better than that of Clasen et al. Indeed, the new similarity solution is valid in all the three regions: the drop, the corner, and the filament regions. Similarity solutions, so obtained, are particularly useful in capillary-breakup rheometry where they are employed to estimate a fluid's extensional viscosity—a material property of viscoelastic fluids that influences greatly the drop formation process.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.