Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-28T15:32:40.707Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamics of bead formation, filament thinning and breakup in weakly viscoelastic jets

Published online by Cambridge University Press:  06 December 2010

A. M. ARDEKANI ,
V. SHARMA  and
G. H. McKINLEY
A. M. ARDEKANI*
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
V. SHARMA
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
G. H. McKINLEY
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

JFM classification

Wakes/Jets: Jets Non-Newtonian Flows: Rheology Non-Newtonian Flows: Viscoelasticity
Type
Papers
Information
Journal of Fluid Mechanics , Volume 665 , 25 December 2010 , pp. 46 - 56
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Anna, S. L., McKinley, G. H., Nguyen, D. A., Sridhar, T., Muller, S. J., Huang, J. & James, D. F. 2001 An interlaboratory comparison of measurements from filament-stretching rheometers using common test fluids. J. Rheol. 45, 83–114.CrossRefGoogle Scholar
Ardekani, A. M., Sharma, V. & McKinley, G. H. 2010 Jetting and breakup of weakly viscoelastic liquids. In 16th US National Congress of Theoretical and Applied Mechanics (USNCTAM2010-912), 17 June–2 July 2010, State College, Pennsylvania.Google Scholar
Basaran, O. A. 1992 Nonlinear oscillation of viscous liquid drops. J. Fluid Mech. 241, 169–198.CrossRefGoogle Scholar
Bauer, H. F. & Eidel, W. 1987 Vibration of a visco-elastic spherical immiscible liquid system. Z. Angew. Math. Mech. 67, 525–535.CrossRefGoogle Scholar
Bhat, P. P., Appathurai, S., Harris, M. T., Pasquali, M., McKinley, G. H. & Basaran, O. A. 2010 Formation of beads-on-a-string structures during breakup of viscoelastic filaments. Nature Phys. 6 (8), 625–631.CrossRefGoogle Scholar
Bird, R. B., Armstrong, R. C. & Hassager, O. 1987 Dynamics of Polymeric Liquids. Wiley.Google Scholar
Bousfield, D. W., Keunings, R., Marrucci, G. & Denn, M. M. 1986 Nonlinear analysis of the surface-tension driven breakup of viscoelastic filaments. J. Non-Newtonian Fluid Mech. 21 (1), 79–97.CrossRefGoogle Scholar
Brenn, G., Liu, Z. & Durst, F. 2000 Linear analysis of the temporal instability of axisymmetrical non-Newtonian liquid jets. Intl J. Multiphase Flow 26, 1621–1644.CrossRefGoogle Scholar
Clasen, C., Eggers, J., Fontelos, M. A., Li, J. & McKinley, G. H. 2006 The beads-on-string structure of viscoelastic threads. J. Fluid Mech. 556, 283–308.CrossRefGoogle Scholar
Eggers, J. 1997 Nonlinear dynamics and breakup of free-surface flows. Rev. Mod. Phys. 69, 865–929.CrossRefGoogle Scholar
Entov, V. M. & Hinch, E. J. 1997 Effect of a spectrum of relaxation times on the capillary thinning of a filament of elastic liquid. J. Non-Newtonian Fluid Mech. 72 (1), 31–53.CrossRefGoogle Scholar
Entov, V. M. & Yarin, A. L. 1984 Influence of elastic stresses on the capillary breakup of dilute polymer solutions. Fluid Dyn. 19, 21–29.CrossRefGoogle Scholar
Fontelos, M. A. & Li, J. 2004 On the evolution and rupture of filaments in Giesekus and FENE models. J. Non-Newtonian Fluid Mech. 118 (1), 1–16.CrossRefGoogle Scholar
Forest, M. G. & Wang, Q. 1990 Change-of-type behavior in viscoelastic slender jet models. J. Theor. Comput. Fluid Dyn. 2, 1–25.CrossRefGoogle Scholar
Giesekus, H. 1982 A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tensorial mobility. J. Non-Newtonian Fluid Mech. 11 (1–2), 69–109.CrossRefGoogle Scholar
Goldin, M., Yerushalmi, J., Pfeffer, R. & Shinnar, R. 1969 Breakup of a laminar capillary jet of a viscoelastic fluid. J. Fluid Mech. 38, 689–711.CrossRefGoogle Scholar
Hoath, S. D., Hutchings, I. M., Martin, G. D., Tuladhar, T. R., Mackley, M. R. & Vadillo, D. 2009 Links between ink rheology, drop-on-demand jet formation, and printability. J. Imaging Sci. Technol. 53, 041208.Google Scholar
Khismatullin, D. B. & Nadim, A. 2001 Shape oscillations of a viscoelastic drop. Phys. Rev. E 63 (6, part 1), 061508.CrossRefGoogle ScholarPubMed
Lamb, H. 1932 Hydrodynamics. Dover.Google Scholar
Li, J. & Fontelos, M. A. 2003 Drop dynamics on the beads-on-string structure for viscoelastic jets: a numerical study. Phys. Fluids 15 (4), 922–937.CrossRefGoogle Scholar
Middleman, S. 1965 Stability of a viscoelastic jet. Chem. Engng Sci. 20, 1037–1040.CrossRefGoogle Scholar
Morrison, N. F. & Harlen, O. G. 2010 Viscoelasticity in inkjet printing. Rheol. Acta 49, 619–632.CrossRefGoogle Scholar
Rayleigh, L. 1879 On the capillary phenomena of jets. Proc. R. Soc. Lond. 29, 71–97.Google Scholar
Rodd, L. E., Scott, T. P., Cooper-White, J. & McKinley, G. H. 2005 Capillary break-up rheometry of low-viscosity elastic fluids. Appl. Rheol. 15, 12–27.CrossRefGoogle Scholar
Schümmer, P. & Tebel, K. H. 1983 A new elongational rheometer for polymer solutions. J. Non-Newtonian Fluid Mech. 12, 331–347.CrossRefGoogle Scholar