Controlling the elongational flow behavior of complex shear-thinning fluids without affecting shear viscosity

  • Walter OswaldEmail author
  • Norbert Willenbacher
Original Contribution


Complex flow fields including high elongational deformation occur in numerous industrial processes such as spraying, coating, fiber spinning, and screen or inkjet printing. Fully exploiting the potential of these technologies suffers from a lack of knowledge regarding how elongational flow properties of the processed fluids affect the results of these operations. Here, we present two strategies that allow for varying the elongational flow behavior independent of shear rheology. First, two acrylic thickener solutions that differ with respect to the fraction of hydrophobic co-monomers and hence with respect to their degree of inter- and intramolecular hydrophobic association were mixed to vary the elongational relaxation time, as determined using capillary breakup elongational rheometry (CaBER), by almost two orders of magnitude without affecting shear viscosity of these solutions in a wide, processing-relevant shear rate range. Second, a substantial increase in the elongational flow resistance was achieved by adding a small amount of plate-like particles without affecting the shear viscosity of these thickener solutions. A fourfold increase of the elongational relaxation time was observed upon the addition of 3.5 vol.% of glass flakes to such a highly shear-thinning system. A similar effect was also observed for an industrial waterborne automotive basecoat due to added aluminum flakes. This work may be useful for product development since the control of extensional viscosity can improve technological applications, and the introduced model systems may therefore be used for systematic, goal-oriented investigations of the relevance of elongational flow properties in the technological processes mentioned above.


Elongational flow CaBER Acrylic thickener Hydrophobic associations Plate-like particles Glass flakes 



The authors would like to thank Georg Wigger and Daniel Briesenick, both from the BASF Coatings GmbH for enabling this investigation and BASF SE and Eckart GmbH for providing the materials. Additionally, we would like to thank Steffen Recktenwald for his help in performing the PIV measurements.


  1. Anna SL, McKinley GH (2001) Elasto-capillary thinning and breakup of model elastic liquids. J Rheol (N Y N Y) 45:115–138. CrossRefGoogle Scholar
  2. Anna SL, McKinley GH, Nguyen DA et al (2001) An interlaboratory comparison of measurements from filament-stretching rheometers using common test fluids. J Rheol (N Y N Y) 45:83–114. CrossRefGoogle Scholar
  3. Arnolds O, Buggisch H, Sachsenheimer D, Willenbacher N (2010) Capillary breakup extensional rheometry (CaBER) on semi-dilute and concentrated polyethyleneoxide (PEO) solutions. Rheol Acta 49:1207–1217. CrossRefGoogle Scholar
  4. Bartolo D, Boudaoud A, Narcy G, Bonn D (2007) Dynamics of non-Newtonian droplets. Phys Rev Lett 99:174502. CrossRefGoogle Scholar
  5. Batchelor GK (1971) The stress generated in a non-dilute suspension of elongated particles by pure straining motion. J Fluid Mech 46:813–829. CrossRefGoogle Scholar
  6. Bazilevskii AV, Entov VM, Lerner MM, Rozhkov AN (1997) Failure of polymer solution filaments. Polym Sci Ser A Chem Phys 39:316–324Google Scholar
  7. Bazilevsky AV, Entov VM, Rozhkov AN (2011) Breakup of a liquid bridge as a method of rheological testing of biological fluids. Fluid Dyn 46:613–622. CrossRefGoogle Scholar
  8. Bergeron V, Bonn D, Martin JY, Vovelle L (2000) Controlling droplet deposition with polymer additives. Nature 405:772–775. CrossRefGoogle Scholar
  9. Brenner H (1974) Rheology of a dilute suspension of axisymmetric Brownian particles. Int J Multiph Flow 1:195–341. CrossRefGoogle Scholar
  10. Christanti Y, Walker LM (2001) Surface tension driven jet break up of strain-hardening polymer solutions. J Nonnewton Fluid Mech 100:9–26. CrossRefGoogle Scholar
  11. Christanti Y, Walker LM (2002) Effect of fluid relaxation time of dilute polymer solutions on jet breakup due to a forced disturbance. J Rheol (N Y N Y) 46:733–748. CrossRefGoogle Scholar
  12. Clasen C (2010) Capillary breakup extensional rheometry of semi-dilute polymer solutions. Korea-Australia Rheol J 5:331–338Google Scholar
  13. Clasen C, Plog JP, Kulicke W-M, Owens M, Macosko C, Scriven LE, Verani M, McKinley GH (2006) How dilute are dilute solutions in extensional flows? J Rheol (N Y N Y) 50:849–881. CrossRefGoogle Scholar
  14. Cogswell FN (1972) Measuring the extensional rheology of polymer melts. Trans Soc Rheol 16:383–403. CrossRefGoogle Scholar
  15. Crassous JJ, Régisser R, Ballauff M, Willenbacher N (2005) Characterization of the viscoelastic behavior of complex fluids using the piezoelastic axial vibrator. J Rheol (N Y N Y) 49:851–863. CrossRefGoogle Scholar
  16. Dexter RW (1996) Measurement of extensional viscosity of polymer solutions and its effects on atomization from a spray nozzle. At Sprays 6:167–191. CrossRefGoogle Scholar
  17. Entov VM, Hinch EJ (1997) Effect of a spectrum of relaxation times on the capillary thinning of a filament of elastic liquid. J Nonnewton Fluid Mech 72:31–53. CrossRefGoogle Scholar
  18. Fernando RH, Xing LL, Glass JE (2000) Rheology parameters controlling spray atomization and roll misting behavior of waterborne coatings. Prog Org Coatings 40:35–38. CrossRefGoogle Scholar
  19. Fuller GG, Cathey CA, Hubbard B, Zebrowski BE (1987) Extensional viscosity measurements for low-viscosity fluids. J Rheol (N Y N Y) 31:235–249. CrossRefGoogle Scholar
  20. Greiciunas E, Wong J, Gorbatenko I, Hall J, Wilson MCT, Kapur N, Harlen OG, Vadillo D, Threlfall-Holmes P (2017) Design and operation of a Rayleigh Ohnesorge jetting extensional rheometer (ROJER) to study extensional properties of low viscosity polymer solutions. J Rheol (N Y N Y) 61:467–476. CrossRefGoogle Scholar
  21. Gupta K, Chokshi P (2017) Stability analysis of bilayer polymer fiber spinning process. Chem Eng Sci 174:277–284. CrossRefGoogle Scholar
  22. Gupta RK, Nguyen DA, Sridhar T (2000) Extensional viscosity of dilute polystyrene solutions: effect of concentration and molecular weight. Phys Fluids 12:1296–1318. CrossRefGoogle Scholar
  23. Hinch EJ, Leal LG (1972) The effect of Brownian motion on the rheological properties of a suspension of non-spherical particles. J Fluid Mech 52:683–712. CrossRefGoogle Scholar
  24. Hoath SD, Vadillo DC, Harlen OG, McIlroy C, Morrison NF, Hsiao WK, Tuladhar TR, Jung S, Martin GD, Hutchings IM (2014) Inkjet printing of weakly elastic polymer solutions. J Nonnewton Fluid Mech 205:1–10. CrossRefGoogle Scholar
  25. Hyun JC (1999) Draw resonance in polymer processing: a short chronology and a new approach. Korea-Aust Rheol J 11:279–285Google Scholar
  26. Jimenez LN, Dinic J, Parsi N, Sharma V (2018) Extensional relaxation time, pinch-off dynamics, and printability of semidilute polyelectrolyte solutions. Macromolecules 51:5191–5208. CrossRefGoogle Scholar
  27. Jogun S, Zukoski CF (1996) Rheology of dense suspensions of plate-like particles. J Rheol (N Y N Y) 40:1211–1232. CrossRefGoogle Scholar
  28. Keshavarz B, Sharma V, Houze EC, Koerner MR, Moore JR, Cotts PM, Threlfall-Holmes P, McKinley GH (2015) Studying the effects of elongational properties on atomization of weakly viscoelastic solutions using Rayleigh Ohnesorge jetting extensional Rheometry (ROJER). J Nonnewton Fluid Mech 222:171–189. CrossRefGoogle Scholar
  29. Kheirandish S, Guybaidullin I, Wohlleben W, Willenbacher N (2008) Shear and elongational flow behavior of acrylic thickener solutions. Rheol Acta 47:999–1013. CrossRefGoogle Scholar
  30. Kheirandish S, Gubaydullin I, Willenbacher N (2009) Shear and elongational flow behavior of acrylic thickener solutions. Part II: effect of gel content. Rheol Acta 48:397–407. CrossRefGoogle Scholar
  31. Kizior TE, Seyer FA (1974) Axial stress in elongational flow of fiber suspension. Trans Soc Rheol 18:271–285. CrossRefGoogle Scholar
  32. Kwag C, Vlachopoulos J (1991) An assessment of Cogswell’s method for measurement of extensional viscosity. Polym Eng Sci 31:1015–1021. CrossRefGoogle Scholar
  33. Lampe J, DiLalla R, Grimaldi J, Rothstein JP (2005) Impact dynamics of drops on thin films of viscoelastic wormlike micelle solutions. J Nonnewton Fluid Mech 125:11–23. CrossRefGoogle Scholar
  34. Le Meins JF, Moldenaers P, Mewis J (2003) Suspensions of monodisperse spheres in polymer melts: particle size effects in extensional flow. Rheol Acta 42:184–190. CrossRefGoogle Scholar
  35. Mansour A, Chigier N (1995) Air-blast atomization of non-Newtonian liquids. J Nonnewton Fluid Mech 58:161–194. CrossRefGoogle Scholar
  36. McKinley GH, Tripathi A (2000) How to extract the Newtonian viscosity from capillary breakup measurements in a filament rheometer. J Rheol (N Y N Y) 44:653–670. CrossRefGoogle Scholar
  37. Meissner J (1985) Rheometry of polymer melts. Annu Rev Fluid Mech 17:45–64. CrossRefGoogle Scholar
  38. Mewis J, Metzner AB (1974) The rheological properties of suspensions of fibres in Newtonian fluids subjected to extensional deformations. J Fluid Mech 62:593. CrossRefGoogle Scholar
  39. Mueller S, Llewellin EW, Mader HM (2010) The rheology of suspensions of solid particles. Proc R Soc A Math Phys Eng Sci 466:1201–1228. CrossRefGoogle Scholar
  40. Ng SL, Mun RP, Boger DV, James DF (1996) Extensional viscosity measurements of dilute solutions of various polymers. J Nonnewton Fluid Mech 65:291–298. CrossRefGoogle Scholar
  41. Niedzwiedz K, Arnolds O, Willenbacher N, Brummer R (2009) How to characterize yield stress fluids with capillary breakup extensional rheometry (CaBER)? Appl Rheol 19:1–10. Google Scholar
  42. Ochowiak M, Broniarz-Press L, Rozanska S, Rozanski J (2012) The effect of extensional viscosity on the effervescent atomization of polyacrylamide solutions. J Ind Eng Chem 18:2028–2035. CrossRefGoogle Scholar
  43. Oswald W, Gödeke L, Ehrhard P, Willenbacher N (2019) An experimental study of the influence of elongational flow behavior and pigmentation on the atomization with a high-speed rotary bell atomizer --- manuscript in preparationGoogle Scholar
  44. Pabst W, Gregorová E, Berthold C (2006) Particle shape and suspension rheology of short-fiber systems. J Eur Ceram Soc 26:149–160. CrossRefGoogle Scholar
  45. Padmanabhan M, Macosko CW, Padmanabhan M (1997) Extensional viscosity from entrance pressure drop measurements. Rheol Acta 36:144–151. CrossRefGoogle Scholar
  46. Papanastasiou TC, Macosko CW, Scriven LE, Chen Z (1987) Fiber spinning of viscoelastic liquid. AICHE J 33:834–842. CrossRefGoogle Scholar
  47. Recktenwald SM, Haward SJ, Shen AQ, Willenbacher N (2019) Heterogeneous flow inside threads of low viscosity fluids leads to anomalous long filament lifetimes. Sci Rep 9:7110. CrossRefGoogle Scholar
  48. Rodd LE, Scott TP, Cooper-White JJ, McKinley GH (2005) Capillary break-up rheometry of low-viscosity elastic fluids. Appl Rheol 15:12–27. CrossRefGoogle Scholar
  49. Rothstein JP, McKinley GH (2002) A comparison of the stress and birefringence growth of dilute, semi-dilute and concentrated polymer solutions in uniaxial extensional flows. J Nonnewton Fluid Mech 108:275–290. CrossRefGoogle Scholar
  50. Rubinstein M, Colby RH (2003) Polymer physics. Oxford University Press, OxfordGoogle Scholar
  51. Sachsenheimer D, Hochstein B, Buggisch H, Willenbacher N (2012) Determination of axial forces during the capillary breakup of liquid filaments - the tilted CaBER method. Rheol Acta 51:909–923. CrossRefGoogle Scholar
  52. Sachsenheimer D, Hochstein B, Willenbacher N (2014) Experimental study on the capillary thinning of entangled polymer solutions. Rheol Acta 53:725–739. CrossRefGoogle Scholar
  53. Santamaría-Holek I, Mendoza CI (2010) The rheology of concentrated suspensions of arbitrarily-shaped particles. J Colloid Interface Sci 346:118–126. CrossRefGoogle Scholar
  54. Shaqfeh ESG, Fredrickson GH (1990) The hydrodynamic stress in a suspension of rods. Phys Fluids A Fluid Dyn 2:7–24. CrossRefGoogle Scholar
  55. Spearot JA, Metzner AB (1972) Isothermal spinning of molten polyethylenes. Trans Soc Rheol 16:495–518. CrossRefGoogle Scholar
  56. Spiegelberg SH, Ables DC, McKinley GH (1996) The role of end-effects on measurements of extensional viscosity in filament stretching rheometers. J Nonnewton Fluid Mech 64:229–267. CrossRefGoogle Scholar
  57. Stelter M, Brenn G, Yarin a L et al (2000) Validation and application of a novel elongational device for polymer solutions. J Rheol (N Y N Y) 44:595–616. CrossRefGoogle Scholar
  58. Stelter M, Brenn G, Yarin AL, Singh RP, Durst F (2002) Investigation of the elongational behavior of polymer solutions by means of an elongational rheometer. J Rheol (N Y N Y) 46:507–527. CrossRefGoogle Scholar
  59. Tembely M, Vadillo D, Mackley MR, Soucemarianadin A (2012) The matching of a “one-dimensional” numerical simulation and experiment results for low viscosity Newtonian and non-Newtonian fluids during fast filament stretching and subsequent break-up. J Rheol (N Y N Y) 56:159–183. CrossRefGoogle Scholar
  60. Teraoka I (2002) Polymer solutions. John Wiley & Sons, Inc., New York, USACrossRefGoogle Scholar
  61. Thielicke W, Stamhuis EJ (2014) PIVlab – towards user-friendly, affordable and accurate digital particle image velocimetry in MATLAB. J Open Res Softw 2.
  62. Thompson JC, Rothstein JP (2007) The atomization of viscoelastic fluids in flat-fan and hollow-cone spray nozzles. J Nonnewton Fluid Mech 147:11–22. CrossRefGoogle Scholar
  63. Tirtaatmadja V, Sridhar T (1993) A filament stretching device for measurement of extensional viscosity. J Rheol (N Y N Y) 37:1081–1102. CrossRefGoogle Scholar
  64. Tirtaatmadja V, McKinley HG, Cooper-White JJ (2006) Drop formation and breakup of low viscosity elastic fluids: effects of molecular weight and concentration. Phys Fluids 18:043101. CrossRefGoogle Scholar
  65. Tropea C, Yarin AL, Foss JF (2007) Springer handbook of experimental fluid mechanics, 1st edn. Springer-Verlag, Berlin HeidelbergCrossRefGoogle Scholar
  66. Trouton FT (1906) On the coefficient of viscous traction and its relation to that of viscosity. Proc R Soc A Math Phys Eng Sci 77:426–440. CrossRefGoogle Scholar
  67. Utracki LA, Lara J (1984) Extensional flow of mica-filled polyethylene. Polym Compos 5:44–51. CrossRefGoogle Scholar
  68. Vadillo DC, Tuladhar TR, Mulji AC, Jung S, Hoath SD, Mackley MR (2010) Evaluation of the inkjet fluid’s performance using the “Cambridge Trimaster” filament stretch and break-up device. J Rheol (N Y N Y) 54:261–282. CrossRefGoogle Scholar
  69. Weinberger CB, Goddard JD (1974) Extensional flow behavior of polymer solutions and particle suspensions in a spinning motion. Int J Multiph Flow 1:465–486. CrossRefGoogle Scholar
  70. Williams PA, English RJ, Blanchard RL, Rose SA, Lyons L, Whitehead M (2008) The influence of the extensional viscosity of very low concentrations of high molecular mass water-soluble polymers on atomisation and droplet impact. Pest Manag Sci 64:497–504. CrossRefGoogle Scholar
  71. Xing LL, Glass JE, Fernando RH (1999) Parameters influencing the spray behavior of waterborne coatings. J Coatings Technol 71:37–50. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Karlsruhe Institute of TechnologyInstitute for Mechanical Process Engineering and MechanicsKarlsruheGermany

Personalised recommendations