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 ...

Drop coalescence is central to diverse processes involving dispersions of drops in industrial, engineering, and scientific realms. During coalescence, two drops first touch and then merge as the liquid neck connecting them grows from initially microscopic scales to a size comparable to the drop diameters. The curvature of the interface is infinite at the point where the drops first make contact, and the flows that ensue as the two drops coalesce are intimately coupled to this singularity in the dynamics. Conventionally, this process has been thought to have just two dynamical regimes: a viscous and an inertial regime with a cross-over region between them. We use experiments and simulations to reveal that a third regime, one that describes the initial dynamics of coalescence for all drop viscosities, has been missed. An argument based on force balance allows the construction of a new coalescence phase diagram.

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.

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