Rheologica Acta

, Volume 48, Issue 6, pp 597–609 | Cite as

Elongational and shear rheology of carbon nanotube suspensions

  • Manish K. Tiwari
  • Alexander V. Bazilevsky
  • Alexander L. Yarin
  • Constantine M. Megaridis
Original Contribution


Rheological behavior of concentrated suspensions of chemical vapor deposition carbon nanotubes in uniaxial elongation and simple shear is studied experimentally and theoretically. Nanotubes are suspended in viscous host liquids—castor oil or its blends with n-decane. The elongational measurements are performed by analyzing self-thinning (due to surface tension effect) liquid threads of nanotube suspensions. A quasi-one-dimensional model is used to describe the self-thinning process, whereas corrections accounting for thread nonuniformity and necking are introduced a posteriori. The effects of nanotube concentration and aspect ratio, viscosity of the suspending liquid, and initial diameter of the self-thinning thread in uniaxial elongation are elucidated. The results for uniaxial elongation are compared with those for simple shear. The correspondence in the results of the shear and elongational measurements is addressed and interpreted. The results conform to the Herschel–Bulkley rheological constitutive equation (i.e., power law fluids with yield stress). However, the yield stress in elongation is about 40% higher than in simple shear flow, which suggests that the original Herschel–Bulkley model need modification with the yield stress being a function of the second invariant of the deviatoric stress tensor. The present effort is the first to study capillary self-thinning of Herschel–Bulkley liquids, which are exemplified here by suspensions of carbon nanotubes.


Nanotube suspension Extentional rheometer Herschel–Bulkley fluid Yield stress Flow curve Extension and shear rheology Capillary thread thinning 



This work was supported by The Volkswagen Foundation. The authors thank Dr. R. Gemeinhart for providing access to the HA-II+ Brookfield shear viscometer.


  1. Aksel N, Heymann L (2007) Rheology of suspensions and emulsions. In: Tropea C et al (eds) Handbook of experimental fluid dynamics. Springer, New YorkGoogle Scholar
  2. Alexandrou AN, Bazilevsky AV et al (2006) On tensile testing of concentrated suspensions. In: The society of rheology 78th annual meeting, Portland, Maine, USA, Portland, Maine, USAGoogle Scholar
  3. Anna SL, McKinley GH (2001) Elasto-capillary thinning and breakup of model elastic liquids. J Rheol 45(1):115–138CrossRefADSGoogle Scholar
  4. Bazilevskiy AV, Rozhkov AN (2006) Dynamics and breakup of zigzag-like jets of polymeric liquids. Fluid Dyn 41(5):493–503CrossRefGoogle Scholar
  5. Bazilevsky AV, Voronkov SI et al (1981) Orientational effects in capillary breakup of jets and threads of dilute polymer solutions. Sov Phys Dokl 257:336–339Google Scholar
  6. Bazilevsky AV, Entov VM et al (1990) Liquid filament microrheometer and some of its applications. In: Proceedings of the 3rd European rheology conference, London, New York Elsevier: London, New York, pp 41–43Google Scholar
  7. Bazilevsky AV, Rozhkov A et al (1994) Stresses in the filaments of polymer solutions. In: Progr. and trends in rheology IV. Proc. 4th Europ. rheology conf., Sevilla, Spain, Steinkopff, Darmstadt Sevilla, Spain, pp 468–470Google Scholar
  8. Bazilevsky AV, Entov VM et al (2001) Breakup of an Oldroyd liquid bridge as a method for testing the rheological properties of polymer solutions. Polym Sci Ser A 43(8):716–726Google Scholar
  9. Brenn G, Yarin AL et al (2006) Capillary thinning of filaments of polymer solutions with surfactants. Colloids Surf A Physicochem Eng Asp 282:68–74CrossRefGoogle Scholar
  10. Doi M, Edwards SF (1986) The theory of polymer dynamics. Clarendon, OxfordGoogle Scholar
  11. Herschel WH, Bulkley R (1926) Konziztensmessungen von gummi-bensollosugen. Kolloid-Z 39(5):291–300CrossRefGoogle Scholar
  12. Hobbie EK, Fry DJ (2007) Rheology of concentrated carbon nanotube suspensions. J Chem Phys 126(14):124907PubMedCrossRefADSGoogle Scholar
  13. Hough LA, Islam MF et al (2004) Viscoelasticity of single wall carbon nanotube suspensions. Phys Rev Lett 93(16):168102PubMedCrossRefADSGoogle Scholar
  14. Huang YY, Ahir SV et al (2006) Dispersion rheology of carbon nanotubes in a polymer matrix. Phys Rev, B 73(14):125422CrossRefADSGoogle Scholar
  15. Husband DM, Aksel N et al (1993) The existence of static yield stresses in suspensions containing noncolloidal particles. J Rheol 37(3):215–235CrossRefADSGoogle Scholar
  16. Kinloch IA, Roberts SA et al (2002) A rheological study of concentrated aqueous nanotube dispersions. Polymer 43(26):7483–7491CrossRefGoogle Scholar
  17. Lin-Gibson S, Pathak JA et al (2004) Elastic flow instability in nanotube suspensions. Phys Rev Lett 92(5):048302CrossRefADSGoogle Scholar
  18. McKinley GH, Tripathi A (2000) How to extract the Newtonian viscosity from capillary breakup measurements in a filament rheometer. J Rheol 44(4):653–670CrossRefADSGoogle Scholar
  19. Miller AF, Donald AM (2002) Surface and interfacial tension of cellulose suspensions. Langmuir 18(26):10155–10162CrossRefGoogle Scholar
  20. Papageorgiou DT (1995) On the breakup of viscous-liquid threads. Phys Fluids 7(8):529–1544Google Scholar
  21. Petrie CJS (1999) The rheology of fibre suspensions. J Non-Newton Fluid Mech 87(2–3):369–402MATHCrossRefGoogle Scholar
  22. Pierson HO (1994) Handbook of carbon, graphite, diamond and fullerenes: properties, processing and applications. Noyes, Park RidgeGoogle Scholar
  23. Reneker DH, Yarin AL et al (2007) Electrospinning of nanofibers from polymer solutions and melts. In: Aref H, van der Giessen E (eds) Advances in applied mechanics, vol 41. Elsevier, Amsterdam, pp 43–195Google Scholar
  24. Rodd LE, Scott TP et al (2005) Capillary break-up rheometry of low-viscosity elastic fluids. Appl Rheol 15:12–27Google Scholar
  25. Rozhkov AN (1983) Dynamics of threads of diluted polymer solutions. J Eng Phys 45(1):72–80CrossRefGoogle Scholar
  26. Stelter M, Brenn G et al (2000) Validation and application of a novel elongational device for polymer solutions. J Rheol 44(4):595–616CrossRefADSGoogle Scholar
  27. Stelter M, Brenn G et al (2002) Investigation of the elongational behavior of polymer solutions by means of an elongational rheometer. J Rheol 46(3):507–527CrossRefADSGoogle Scholar
  28. Szczech JB, Megaridis CM et al (2002) Fine-line conductor manufacturing using drop-on-demand PZT printing technology. IEEE Trans Electron Packag Manuf 25(1):26–33CrossRefGoogle Scholar
  29. Szczech JB, Megaridis CM et al (2004) Ink jet processing of metallic nanoparticle suspensions for electronic circuitry fabrication. Microscale Thermophys Eng 8(5):327–339CrossRefGoogle Scholar
  30. Wunderlich T, Stelter M et al (2000) Shear and extensional rheological investigations in solutions of grafted and ungrafted polysaccharides. J Appl Polym Sci 77(16):3200–3209CrossRefGoogle Scholar
  31. Xue HS, Fan JR et al (2006) The interface effect of carbon nanotube suspension on the thermal performance of a two-phase closed thermosyphon. J Appl Phys 100(12):104909CrossRefADSGoogle Scholar
  32. Yang Y, Grulke EA et al (2005) Rheological behavior of carbon nanotube and graphite nanoparticle dispersions. J Nanosci Nanotechnol 5(5):571–579PubMedCrossRefGoogle Scholar
  33. Yang Y, Grulke EA et al (2006) Thermal and rheological properties of carbon nanotube-in-oil dispersions. J Appl Phys 99(13):114307CrossRefADSGoogle Scholar
  34. Yarin AL (1993) Free liquid jets and films: hydrodynamics and rheology. Longman, Harlow, and Wiley, New YorkMATHGoogle Scholar
  35. Yarin AL, Gottlieb O et al (1997) Chaotic rotation of triaxial ellipsoids in simple shear flow. J Fluid Mech 340:83–100MATHCrossRefADSMathSciNetGoogle Scholar
  36. Yarin AL, Zussman E et al (2004) Elongational behavior of gelled propellant simulants. J Rheol 48(1):101–116CrossRefADSGoogle Scholar
  37. Zussman E, Yarin AL et al (2007) Age- and flow-dependency of salivary viscoelasticity. J Dent Res 86(4):281–285PubMedGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Manish K. Tiwari
    • 1
  • Alexander V. Bazilevsky
    • 1
  • Alexander L. Yarin
    • 1
  • Constantine M. Megaridis
    • 1
  1. 1.Department of Mechanical and Industrial EngineeringUniversity of Illinois at ChicagoChicagoUSA

Personalised recommendations