Formation of beads-on-a-string structures during break-up of viscoelastic filaments

Abstract

Break-up 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 break-up 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 occurs only 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.

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Figure 1: Using a ‘digital rheometer’ to measure the stringiness or pituity of various complex liquids, and filament morphologies near pinch-off.
Figure 2: Liquid-bridge definition sketch.
Figure 3: Filament thinning and satellite bead formation in Newtonian and Oldroyd-B filaments.
Figure 4: Influence of fluid inertia on the dynamics of satellite bead formation, and formation of sub-satellite beads in viscoelastic filaments.
Figure 5: Phase diagram depicting the regions showing different BOAS morphologies in the De and Oh space for Oldroyd-B filaments with β=0.6 and Λ=3.

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Acknowledgements

This work was supported by the National Science Foundation Engineering Research Center for Structured Organic Particulate Systems (NSF ERC-SOPS)(EEC-0540855) at Rutgers, Purdue, NJIT and UPRM. G.H.M., acknowledges support from the Nanoscale Interdisciplinary Reasearch Thrust on ‘Directed Self-assembly of Suspended Polymer Fibers’ (NSF-DMS0506941.

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P.P.B. planned research, carried out calculations, analysed data and wrote the article; S.A. carried out calculations and analysed data; M.T.H. planned research; M.P. planned research, analysed data and wrote the article; G.H.M. carried out experiments, analysed data and wrote the article; O.A.B. planned research, analysed data and wrote the article.

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Correspondence to Osman A. Basaran.

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Bhat, P., Appathurai, S., Harris, M. et al. Formation of beads-on-a-string structures during break-up of viscoelastic filaments. Nature Phys 6, 625–631 (2010). https://doi.org/10.1038/nphys1682

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