Rheologica Acta

, Volume 58, Issue 9, pp 573–590 | Cite as

Investigating the dynamics of droplet breakup in a microfluidic cross-slot device for characterizing the extensional properties of weakly-viscoelastic fluids

  • Kristin A. Marshall
  • Travis W. WalkerEmail author
Original Contribution


A microfluidic device, deemed the Plateau-Rayleigh microfluidic extensional rheometer (PRIMER), is presented that uses a cross-slot geometry to observe a two-phase droplet-breakup event in which the viscoelastic fluid is in the dispersed (or droplet) phase. For viscoelastic fluids, we report that a cylindrical filament forms between droplet segments with a diameter that decays exponentially in time. In optically tracking this decay, both transient extensional viscosity and extensional relaxation times can be evaluated. For validating and optimizing the device, a range of poly(ethylene oxide) (PEO) solutions and Newtonian solutions were tested. Comparisons of the evolution profiles as a result of the presence of elasticity are made, and these results are compared with the results from dripping-onto-a-substrate (DoS), another emerging extensional technique.


Breakup Viscoelasticity Extensional flow Drop deformation 



The authors would like to thank Dr. Skip Rochefort, Dr. Alex Yokochi, and Dr. Adam Higgins for their contributions to this work. The authors would also like to thank Oregon State University’s Johnson Summer Internship program and the Saturday Academy’s Apprenticeships in Science and Engineering (ASE) program for supplying talented interns to participate in this work, specifically the authors would like to thank Shelley Haug, Aleesha Liedtke, Katie Moreno, Anika Todt, and Zach Wallace for their assistance in running preliminary experiments. KAM and TWW would also like to thank Hewlett Packard Inc. and the Diversity Pipeline Fellowship at Oregon State University for financial support.


  1. Amarouchene Y, Bonn D, Meunier J, Kellay H (2001) Inhibition of the finite-time singularity during droplet fission of a polymeric fluid. Phys Rev Lett 86(16):3558Google Scholar
  2. Anna SL, McKinley GH (2001) Elasto-capillary thinning and breakup of model elastic liquids. J Rheol 45 (1):115–138Google Scholar
  3. Anna SL, McKinley GH (2008) Effect of a controlled pre-deformation history on extensional viscosity of dilute polymer solutions. Rheol Acta 47(8):841–859Google Scholar
  4. Anna SL, McKinley GH, Nguyen DA, Sridhar T, Muller SJ, Huang J, James DF (2001) An interlaboratory comparison of measurements from filament-stretching rheometers using common test fluids. J Rheol 45(1):83–114Google Scholar
  5. Ardekani AM, Sharma V, McKinley GH (2010) Dynamics of bead formation, filament thinning and breakup in weakly viscoelastic jets. J Fluid Mech 665:46–56Google Scholar
  6. Arratia PE, Cramer LA, Gollub JP, Durian DJ (2009) The effects of polymer molecular weight on filament thinning and drop breakup in microchannels, vol 11Google Scholar
  7. Arratia PE, Gollub JP, Durian DJ (2008) Polymeric filament thinning and breakup in microchannels, vol 77Google Scholar
  8. Basaran OA (2002) Small-scale free surface flows with breakup: drop formation and emerging applications. AIChE J 48(9):1842–1848Google Scholar
  9. Bazilevskii AV, Entov VM, Rozhkov AN (2001) Breakup of an oldroyd liquid bridge as a method for testing the rheological properties of polymer solutions. Polym Sci Ser A 43(7):716–726Google Scholar
  10. Bazilevsky AV, Entov VM, Rozhkov AN (1990) Liquid filament microrheometer and some of its applications. In: Third European Rheology Conference and Golden Jubilee Meeting of the British Society of Rheology. Springer, pp 41–43Google Scholar
  11. Bazilevsky AV, Entov VM, Rozhkov AN (2011) Breakup of a liquid bridge as a method of rheological testing of biological fluids. Fluid Dyn 46(4):613Google Scholar
  12. Bhat PP, Appathurai S, Harris MT, Pasquali M, McKinley GH, Basaran OA (2010) Formation of beads-on-a-string structures during break-up of viscoelastic filaments. Nat Phys 6(8):625– 631Google Scholar
  13. Brandrup J, Immergut EH, Grulke EA, Abe A, Bloch DR (1989) Polymer handbook, vol 7, WileyGoogle Scholar
  14. Campo-Deano L, Clasen C (2010) The slow retraction method (SRM) for the determination of ultra-short relaxation times in capillary breakup extensional rheometry experiments. J Non-Newtonian Fluid Mech 165 (23):1688–1699Google Scholar
  15. Christanti Y, Walker LM (2001) Surface tension driven jet break up of strain-hardening polymer solutions. J Non-Newtonian Fluid Mech 100(1):9–26Google Scholar
  16. Christanti Y, Walker LM (2002) Effect of fluid relaxation time of dilute polymer solutions on jet breakup due to a forced disturbance. J Rheol 46(3):733–748Google Scholar
  17. Christopher GF, Anna SL (2009) Passive breakup of viscoelastic droplets and filament self-thinning at a microfluidic T-junction. J Rheol 53(3):663–683Google Scholar
  18. Clasen C, Eggers J, Fontelos MA, Li J, McKinley GH (2006a) The beads-on-string structure of viscoelastic threads. J Fluid Mech 556:283–308Google Scholar
  19. Clasen C, Plog JP, Kulicke W-M, Owens M, Macosko C, Scriven LE, Verani M, McKinley GH (2006b) How dilute are dilute solutions in extensional flows? J Rheol 50(6):849–881Google Scholar
  20. Clasen C, Verani M, Plog JP, McKinley GH, Kulicke WM (2004) Effects of polymer concentration and molecular weight on the dynamics of visco-elasto-capillary breakupGoogle Scholar
  21. Cogswell FN (1972) Measuring the extensional rheology of polymer melts. Trans Soc Rheol 16(3):383–403Google Scholar
  22. Collier JR, Romanoschi O, Petrovan S (1998) Elongational rheology of polymer melts and solutions. J Appl Polym Sci 69(12):2357–2367Google Scholar
  23. Cooper-White JJ, Fagan JE, Tirtaatmadja V, Lester DR, Boger DV (2002) Drop formation dynamics of constant low-viscosity, elastic fluids. J Non-Newtonian Fluid Mech 106(1):29–59Google Scholar
  24. de Gans B-J, Duineveld PC, Schubert US (2004) Inkjet printing of polymers: state of the art and future developments. Adv Mater 16(3):203–213Google Scholar
  25. De Gennes PG (1974) Coil-stretch transition of dilute flexible polymers under ultrahigh velocity gradients. J Chem Phys 60(12):5030–5042Google Scholar
  26. De Menech M, Garstecki P, Jousse F, Stone HA (2008) Transition from squeezing to dripping in a microfluidic t-shaped junction. J Fluid Mech 595:141–161Google Scholar
  27. Dinic J, Zhang Y, Jimenez LN, Sharma V (2015) Extensional relaxation times of dilute, aqueous polymer solutions. ACS Macro Lett 4(7):804–808Google Scholar
  28. Dinic J, Jimenez LN, Sharma V (2017) Pinch-off dynamics and dripping-onto-substrate (DoS) rheometry of complex fluids. Lab Chip 17:460–473Google Scholar
  29. Dylla-Spears R, Townsend JE, Jen-Jacobson L, Sohn LL, Muller SJ (2010) Single-molecule sequence detection via microfluidic planar extensional flow at a stagnation point. Lab Chip 10(12):1543–1549Google Scholar
  30. Entov VM, Hinch EJ (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):31–53Google Scholar
  31. Ewoldt RH, Johnston MT, Caretta LM (2015) Experimental challenges of shear rheology: how to avoid bad data. In: Complex fluids in biological systems. Springer, pp 207–241Google Scholar
  32. Feng J, Leal LG (2000) Transient extension and relaxation of a dilute polymer solution in a four-roll mill. J Non-Newtonian Fluid Mech 90(1):117–123Google Scholar
  33. Flory PJ (1953) Principles of polymer chemistry. Cornell University Press, New YorkGoogle Scholar
  34. Friend J, Yeo L (2010) Fabrication of microfluidic devices using polydimethylsiloxane, vol 4, BiomicrofluidicsGoogle Scholar
  35. Fuller GG, Cathey CA, Hubbard B, Zebrowski BE (1987) Extensional viscosity measurements for low-viscosity fluids. J Rheol 31(3):235–249Google Scholar
  36. Galindo-Rosales FJ, Alves MA, Oliveira MSN (2013) Microdevices for extensional rheometry of low viscosity elastic liquids: a review. Microfluid Nanofluid 14(1-2):1–19Google Scholar
  37. Garstecki P, Fuerstman MJ, Stone HA, Whitesides GM (2006) Formation of droplets and bubbles in a microfluidic T-junction—scaling and mechanism of break-up. Lab Chip 6(3):437–446Google Scholar
  38. Graessley WW (1980) Polymer chain dimensions and the dependence of viscoelastic properties on concentration, molecular weight and solvent power. Polymer 21(3):258–262Google Scholar
  39. Gyr A, Bewersdorff HW (2013) Drag reduction of turbulent flows by additives, vol 32, Springer, BerlinGoogle Scholar
  40. Harrison GM, Boger DV (2000) Well-characterized low viscosity elastic liquids. Appl Rheol 10(4):166–177Google Scholar
  41. Haward SJ (2014) Characterization of hyaluronic acid and synovial fluid in stagnation point elongational flow. Biopolymers 101(3):287–305Google Scholar
  42. Haward SJ, Oliveira MSN, Alves MA, McKinley GH (2012) Optimized cross-slot flow geometry for microfluidic extensional rheometry, vol 109Google Scholar
  43. Hinch EJ (1974) Mechanical models of dilute polymer solutions for strong flows with large polymer deformations. Polymères et Lubrification, pp 351–372Google Scholar
  44. Haward SJ (2016) Microfluidic extensional rheometry using stagnation point flow, vol 10Google Scholar
  45. Hoath SD, Hsiao WK, Martin GD, Jung S, Butler SA, Morrison NF, Harlen OG, Yang LS, Bain CD, Hutchings IM (2015) Oscillations of aqueous pedot Pss fluid droplets and the properties of complex fluids in drop-on-demand inkjet printing. J Non-Newtonian Fluid Mech 223:28–36Google Scholar
  46. Hudson SD, Phelan FR Jr, Handler MD, Cabral JT, Migler KB, Amis EJ (2004) Microfluidic analog of the four-roll mill. Appl Phys Lett 85(2):335–337Google Scholar
  47. Husny J, Cooper-White JJ (2006) The effect of elasticity on drop creation in t-shaped microchannels. J Non-Newtonian Fluid Mech 137(1):121–136Google Scholar
  48. James DF, Walters K (1993) A critical appraisal of available methods for the measurement of extensional properties of mobile systems. In: Techniques in rheological measurement. Springer, pp 33–53Google Scholar
  49. Jones DM, Walters K (1989) The behaviour of polymer solutions in extension-dominated flows, with applications to enhanced oil recovery. Rheol Acta 28(6):482–498Google Scholar
  50. 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 Non-Newtonian Fluid Mech 222:171–189Google Scholar
  51. Kolte MI, Szabo P (1999) Capillary thinning of polymeric filaments. J Rheol 43(3):609–625Google Scholar
  52. Lee JS, Dylla-Spears R, Teclemariam NP, Muller SJ (2007) Microfluidic four-roll mill for all flow types, vol 90Google Scholar
  53. Li J, Fontelos MA (2003) Drop dynamics on the beads-on-string structure for viscoelastic jets: a numerical study. Phys Fluids 15(4):922–937Google Scholar
  54. Liang RF, Mackley MR (1994) Rheological characterization of the time and strain dependence for polyisobutylene solutions. J Non-Newtonian Fluid Mech 52(3):387–405Google Scholar
  55. Link DR, Anna SL, Weitz DA, Stone HA (2004) Geometrically mediated breakup of drops in microfluidic devices, vol 92Google Scholar
  56. Lister JR, Stone HA (1998) Capillary breakup of a viscous thread surrounded by another viscous fluid. Phys Fluids 10(11):2758–2764Google Scholar
  57. Macosko CW (1994) Rheology: principles, measurements, and applications. Wiley-VCH, New JerseyGoogle Scholar
  58. Marshall KA, Liedtke AM, Todt AH, Walker TW (2017) Extensional rheometry with a handheld mobile device. Exp Fluids 6(58):1–9Google Scholar
  59. Matta JE, Tytus RP (1990) Liquid stretching using a falling cylinder. J Non-Newtonian Fluid Mech 35 (2-3):215–229Google Scholar
  60. Mckinley GH (2005a) Dimensionless groups for understanding free surface flows of complex fluids. Society of Rheology Bulletin 2005:6–9Google Scholar
  61. Mckinley GH (2005b) Visco-elasto-capillary thinning and break-up of complex fluids. Rheology Rev 2005(3):1–48Google Scholar
  62. McKinley GH, Sridhar T (2002) Filament-stretching rheometry of complex fluids. Ann Rev Fluid Mech 34 (1):375–415Google Scholar
  63. McKinley GH, Tripathi A (2000) How to extract the newtonian viscosity from capillary breakup measurements in a filament rheometer. J Rheol 44(3):653–670Google Scholar
  64. MicroChem (n.d.) Permanent epoxy negative photoresist processing guidelines for: SU-8 2100 and SU-8 2150.
  65. Miller E, Clasen C, Rothstein JP (2009) The effect of step-stretch parameters on capillary breakup extensional rheology (CaBER) measurements. Rheol Acta 48(6):625–639Google Scholar
  66. Morrison NF, Harlen OG (2010) Viscoelasticity in inkjet printing. Rheol Acta 49(6):619–632Google Scholar
  67. Nguyen DA, Gupta RK, Sridhar T (1990) Experimental results and constitutive modeling of the extensional flow of M1. J Non-Newtonian Fluid Mech 35(2):207–214Google Scholar
  68. Oliveira MSN, McKinley GH (2005) Iterated stretching and multiple beads-on-a-string phenomena in dilute solutions of highly extensible flexible polymers, vol 17Google Scholar
  69. Oliveira MSN, Yeh R, McKinley GH (2006) Iterated stretching, extensional rheology and formation of beads-on-a-string structures in polymer solutions. J Non-Newtonian Fluid Mech 137(1):137–148Google Scholar
  70. Öttinger HC (2012) Stochastic processes in polymeric fluids: tools and examples for developing simulation algorithms. Springer Science & Business MediaGoogle Scholar
  71. Paterson RW, Abernathy FH (1970) Turbulent flow drag reduction and degradation with dilute polymer solutions. J Fluid Mech 43(4):689–710Google Scholar
  72. Petrie CJS (2006) Extensional viscosity: a critical discussion. J Non-Newtonian Fluid Mech 137(1):15–23Google Scholar
  73. Renardy M (1995) A numerical study of the asymptotic evolution and breakup of Newtonian and viscoelastic jets. J Non-Newtonian Fluid Mech 59(2-3):267–282Google Scholar
  74. Rodd LE, Scott TP, Cooper-White JJ, McKinley GH (2005) Capillary break-up rheometry of low-viscosity elastic fluids. Appl Rheol 15(1):12–27Google Scholar
  75. Savins JG (1964) Drag reduction characteristics of solutions of macromolecules in turbulent pipe flow. Soc Pet Eng J 4(03):203–214Google Scholar
  76. Schümmer P, Tebel KH (1983) A new elongational rheometer for polymer solutions. J Non-Newtonian Fluid Mech 12(3):331–347Google Scholar
  77. Schummer P, Tebel KH (1982) Production of monodispersed drops by forced disturbance of a free jet. German Chemical Engineering 5:209–220Google Scholar
  78. Sharma V, Haward SJ, Serdy J, Keshavarz B, Soderlund A, Threlfall-Holmes P, McKinley GH (2015) The rheology of aqueous solutions of ethyl hydroxy-ethyl cellulose (EHEC) and its hydrophobically modified analogue (hmEHEC): extensional flow response in capillary break-up, jetting (ROJER) and in a cross-slot extensional rheometer. Soft Matter 11(16):3251–3270Google Scholar
  79. Sousa PC, Vega EJ, Sousa RG, Montanero JM, Alves MA (2017) Measurement of relaxation times in extensional flow of weakly viscoelastic polymer solutions. Rheol Acta 56(1):11–20Google Scholar
  80. Spiegelberg SH, Ables DC, McKinley GH (1996) The role of end-effects on measurements of extensional viscosity in filament stretching rheometers. J Non-Newtonian Fluid Mech 64(2):229–267Google Scholar
  81. Stelter M, Brenn G, Yarin AL, Singh RP, Durst F (2000) Validation and application of a novel elongational device for polymer solutions. J Rheol 44(3):595–616Google Scholar
  82. Stone HA (1994) Dynamics of drop deformation and breakup in viscous fluids. Ann Rev Fluid Mech 26 (1):65–102Google Scholar
  83. Stone HA, Leal LG (1989) Relaxation and breakup of an initially extended drop in an otherwise quiescent fluid. J Fluid Mech 198:399–427Google Scholar
  84. Stone HA, Leal GL (1990) The effects of surfactants on drop deformation and breakup. J Fluid Mech 220:161–186Google Scholar
  85. Stone HA, Bentley BJ, Leal LG (1986) An experimental study of transient effects in the breakup of viscous drops. J Fluid Mech 173:131–158Google Scholar
  86. Teraoka I (2002) Models of polymer chains. Wiley, New JerseyGoogle Scholar
  87. Tirtaatmadja V, McKinley GH, Cooper-White JJ (2006) Drop formation and breakup of low viscosity elastic fluids: effects of molecular weight and concentration, vol 18Google Scholar
  88. Tjahjadi M, Stone HA, Ottino JM (1992) Satellite and subsatellite formation in capillary breakup. J Fluid Mech 243:297– 317Google Scholar
  89. Tuladhar TR, Mackley MR (2008) Filament stretching rheometry and break-up behaviour of low viscosity polymer solutions and inkjet fluids. J Non-Newtonian Fluid Mech 148(1):97– 108Google Scholar
  90. van Steijn V, Kleijn CR, Kreutzer MT (2010) Predictive model for the size of bubbles and droplets created in microfluidic T-junctions. Lab Chip 10(19):2513–2518Google Scholar
  91. Virk PS (1975) Drag reduction fundamentals. AIChE J 21(4):625–656Google Scholar
  92. Wagner C, Bourouiba L, McKinley GH (2015) An analytic solution for capillary thinning and breakup of fene-p fluids. J Non-Newtonian Fluid Mech 218:53–61Google Scholar
  93. Wagner C, Amarouchene Y, Bonn D, Eggers J (2005) Droplet detachment and satellite bead formation in viscoelastic fluids, vol 95Google Scholar
  94. Walker TW, Hsu TT, Fitzgibbon S, Frank CW, Mui DSL, Ji Z, Mendiratta A, Fuller GG (2014) Enhanced particle removal using viscoelastic fluids. J Rheol 58(1):63–88Google Scholar
  95. Wever DAZ, Picchioni F, Broekhuis AA (2011) Polymers for enhanced oil recovery: a paradigm for structure–property relationship in aqueous solution. Prog Polym Sci 36(11):1558– 1628Google Scholar
  96. Xu D, Sanchez-Romaguera V, Barbosa S, Travis W, de Wit J, Swan P, Yeates SG (2007) Inkjet printing of polymer solutions and the role of chain entanglement. J Mater Chem 17(46):4902– 4907Google Scholar
  97. Xu JH, Li SW, Tan J, Wang YJ, Luo GS (2006) Preparation of highly monodisperse droplet in a T-junction microfluidic device. AIChE J 52(9):3005–3010Google Scholar
  98. Xu JH, Li SW, Tan J, Luo GS (2008) Correlations of droplet formation in T-junction microfluidic devices: from squeezing to dripping. Microfluid Nanofluid 5(6):711–717Google Scholar
  99. Yarin AL (1993) Free liquid jets and films: hydrodynamics and rheology. Longman Publishing Group, HarlowGoogle Scholar
  100. Zhong L, Oostrom M, Truex MJ, Vermeul VR, Szecsody JE (2013) Rheological behavior of xanthan gum solution related to shear thinning fluid delivery for subsurface remediation. J Hazard Mater 244:160–170Google Scholar

Copyright information

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

Authors and Affiliations

  1. 1.School of Chemical, Biological, and Environmental EngineeringOregon State UniversityCorvallisUSA
  2. 2.Department of Chemical and Biological EngineeringSouth Dakota School of Mines and TechnologyRapid CityUSA

Personalised recommendations