Advertisement

Rheologica Acta

, Volume 48, Issue 2, pp 191–200 | Cite as

A comparison of three different methods for measuring both normal stress differences of viscoelastic liquids in torsional rheometers

  • Mataz Alcoutlabi
  • S. G. Baek
  • J. J. MagdaEmail author
  • Xiangfu Shi
  • S. A. Hutcheson
  • G. B. McKenna
Original Contribution

Abstract

A novel pressure sensor plate (normal stress sensor (NSS) from RheoSense, Inc.) was adapted to an Advanced Rheometrics Expansion System rheometer in order to measure the radial pressure profile for a standard viscoelastic fluid, a poly(isobutylene) solution, during cone–plate and parallel-plate shearing flows at room temperature. We observed in our previous experimental work that use of the NSS in cone-and-plate shearing flow is suitable for determining the first and second normal stress differences N 1 and N 2 of various complex fluids. This is true, in part, because the uniformity of the shear rate at small cone angles ensures the existence of a simple linear relationship between the pressure [i.e., the vertical diagonal component of the total stress tensor (Π22)] and the logarithm of the radial position r (Christiansen and coworkers, Magda et al.). However, both normal stress differences can also be calculated from the radial pressure distribution measured in parallel-plate torsional flows. This approach has rarely been attempted, perhaps because of the additional complication that the shear rate value increases linearly with radial position. In this work, three different methods are used to investigate N 1 and N 2 as a function of shear rate in steady shear flow. These methods are: (1) pressure distribution cone–plate (PDCP) method, (2) pressure distribution parallel-plate (PDPP) method, and (3) total force cone–plate parallel-plate (TFCPPP) method. Good agreement was obtained between N 1 and N 2 values obtained from the PDCP and PDPP methods. However, the measured N 1 values were 10–15% below the certified values for the standard poly(isobutylene) solution at higher shear rates. The TFCPPP method yielded N 1 values that were in better agreement with the certified values but gave positive N 2 values at most shear rates, in striking disagreement with published results for the standard poly(isobutylene) solution.

Keywords

Viscoelasticity Normal stresses Rheology 

Notes

Acknowledgements

Acknowledgment is made to the Donors of the American Chemical Society Petroleum Research Fund for partial support of this research, grants 45968-AC9 for M.A. and J.J.M. and 40615-AC7 for the McKenna research group at TTU. The McKenna research group also acknowledges the John R. Bradford Endowment at TTU for partial support of this work. We thank RheoSense, Inc. (San Ramon, CA, USA) for providing the pressure sensor plate adapted to the ARES Rheometer at Texas Tech University.

References

  1. Adams N, Lodge AS (1964) A cone-and-plate and parallel-plate pressure distribution apparatus for determining normal stress differences in steady shear flow. Phil Trans Royal Soc London A256:149–184CrossRefADSGoogle Scholar
  2. Alvarez GA, Lodge AS, Cantow H-J (1985) Measurement of the first and second normal stress differences: correlation of four experiments on a polyisobutylene/decalin solution “D1”. Rheol Acta 24:368–376CrossRefGoogle Scholar
  3. Baek S-G, Magda JJ (2003) Monolithic rheometer plate fabricated using silicon micromachining technology and containing miniature pressure sensors for N 1 and N 2 measurement. J Rheol 47:1249–1260CrossRefADSGoogle Scholar
  4. Beavers GS, Joseph DD (1975) Rotating rod viscometer. J Fluid Mech 69:475–511zbMATHCrossRefGoogle Scholar
  5. Bird RB, Armstrong RC, Hassager O (1987) Dynamics of polymeric liquids vol. 1, 2nd edn. Wiley, New York, pp 521–524Google Scholar
  6. Broadbent JM, Kaye A, Lodge AS, Vale DG (1968) Possible systematic error in the measurement of normal stress differences in polymer solutions in steady shear flow. Nature 217:55–56CrossRefADSGoogle Scholar
  7. Brown EF, Burghardt WR, Kahvand H, Venerus DC (1995) Comparison of optical and mechanical measurements of the second normal stress difference relaxation following step strain. Rheol Acta 34:221–234CrossRefGoogle Scholar
  8. Debbaut B, Avalosse T, Dooley J, Hughes K (1997) On the development of secondary motions in straight channels induced by the second normal stress difference: experiments and simulations. J Non-Newton Fluid Mech 69:255–271CrossRefGoogle Scholar
  9. Dutcher CS, Venerus DC (2008) Compliance effects on the torsional flow of a viscoelastic fluid. J Non-Newton Fluid Mech 150:154–161CrossRefGoogle Scholar
  10. Feigl K, Ottinger HC (1994) The flow of a LDPE melt through an axisymmetric contraction: a numerical study and comparison to experimental results. J Rheol 38:847–874CrossRefADSGoogle Scholar
  11. Gao HW, Ramachandran S, Christiansen EB (1981) Dependency of the steady-state and transient viscosity and first and second normal stress differences functions on molecular weight for linear mono and polydisperse polystyrene solutions. J Rheol 25:213CrossRefADSGoogle Scholar
  12. Ginn RF, Metzner A (1969) Measurement of stresses developed in steady laminar shearing flows of viscoelastic media. Trans Soc Rheol 13(4):429–453CrossRefGoogle Scholar
  13. Huang W (2007) University of Utah (in press)Google Scholar
  14. Hutcheson SA, Shi XF, McKenna GB (2004) Performance comparison of a custom strain gage based load cell with a rheometric series force rebalance transducer. Paper presented at the annual technical conference (ANTEC) of the society of plastics engineers, Chicago, IL, 16–20 May, pp 2272–2276Google Scholar
  15. Kannan RM, Kornfield JA (1992) The third-normal stress difference in entangled melts: quantitative stress-optical measurements in oscillatory shear. Rheol Acta 31:535–544CrossRefGoogle Scholar
  16. Keentok M, Tanner RI (1982) Cone-plate and parallel plate rheometry of some polymer solutions. J Rheol 26(3):301–311CrossRefADSGoogle Scholar
  17. Kotaka K, Kurata M, Tamura M (1959) Normal stress effect in polymer solution. J Appl Phys 30:1705–1712CrossRefADSGoogle Scholar
  18. Lee CS, Tripp BC, Magda JJ (1992) Does N 1 or N 2 control the onset of edge fracture? Rheol Acta 31:306–308CrossRefGoogle Scholar
  19. Lee M, Alcoutlabi M, Magda JJ, Dibble C, Solomon MJ, Shi X, McKenna GB (2006) The effect of the shear-thickening transition of model colloidal spheres on the sign of N 1 and on the radial pressure profile in torsional shear flows. J Rheol 50:293–311CrossRefADSGoogle Scholar
  20. Magda JJ, Lou J, Baek S-G, DeVries KL (1991a) Second normal stress difference of a Boger fluid. Polymer 32:2000–2009CrossRefGoogle Scholar
  21. Magda JJ, Baek S-G, DeVries KL, Larson RG (1991b) Shear flows of liquid crystal polymers: measurements of the second normal stress difference and the Doi molecular theory. Macromol 24:4460–4468CrossRefGoogle Scholar
  22. Magda JJ, Lee C-S, Muller SJ, Larson RG (1993) Rheology, flow instabilities, and shear-induced diffusion in polystyrene solutions. Macromolecules 26:1696–1706CrossRefGoogle Scholar
  23. Meissner J, Barbella RW, Hostettler J (1989) Measuring normal stress differences in polymer melt shear flow. J Rheol 33:843–864CrossRefGoogle Scholar
  24. Miller MJ, Christiansen EB (1972) Stress state of elastic fluids in viscometric flow. AIChE 18:600–608CrossRefGoogle Scholar
  25. Niemiec JM, Pesce J-J, McKenna GB (1996) Anomalies in the normal force measurement when using a force rebalance transducer. J Rheol 40:323–334CrossRefADSGoogle Scholar
  26. Ohl N, Gleissle W (1992) The second normal stress difference for pure and highly filled viscoelastic fluids. Rheol Acta 31:294–305CrossRefGoogle Scholar
  27. Penn RW, Kearsley EA (1976) The scaling law for finite torsion of elastic cylinders. Trans Soc Rheol 20:227–238CrossRefGoogle Scholar
  28. Schweizer T (2002) Measurement of the first and second normal stress differences in a polystyrene melt with a cone and partitioned plate tool. Rheol Acta 41:337–344CrossRefGoogle Scholar
  29. Schweizer T, Bardow A (2006) The role of instrument compliance in normal force measurement of polymer melts. Rheol Acta 45:393–402CrossRefGoogle Scholar
  30. Schweizer T, Stockli M (2008) Departure from linear velocity profile at the surface of polystyrene melts during shear in cone–plate geometry. J Rheol 52:713–727CrossRefADSGoogle Scholar
  31. Shipman RGW, Denn MM, Keunings R (1991) Free-surface effects in torsional parallel-plate rheometry. Ind Eng Chem Res 30:918–922CrossRefGoogle Scholar
  32. Soskey PR, Winter HH (1984) Large step shear strain experiments with parallel-disk rotational rheometers. J Rheol 28:625–645CrossRefADSGoogle Scholar
  33. Sui C, McKenna GB (2007a) Nonlinear viscoelastic properties of branched polyethylene in reversing flows. J Rheol 51:341–365CrossRefADSGoogle Scholar
  34. Sui C, McKenna GB (2007b) Instability of entangled polymers in cone and plate rheometry. Rheol Acta 46:877–888CrossRefGoogle Scholar
  35. Takahashi T, Shirakashi M, Miyamoto K, Fuller GG (2002) Development of a double-beam rheo-optical analyzer for full tensor measurement of optical anisotropy in complex fluid flow. Rheol Acta 41:448–455CrossRefGoogle Scholar
  36. Venerus DC (2007) Free surface effects on normal stress measurements in cone and plate flow. Appl Rheol 17:36494-1–36494-6Google Scholar
  37. Vrentas CM, Graessley WW (1981) Relaxation of shear and normal stress components in step-strain experiments. J Non-Newtonian Fluid Mech 9:339–355CrossRefGoogle Scholar
  38. Walters K (1983) The second-normal-stress difference project. IUPAC Macro 83, Plenary and Invited Lectures Part II, 227–237Google Scholar
  39. Zapas LJ, McKenna GB, Brenna A (1989) An analysis of the corrections to the normal force response for the cone and plate geometry in single step stress relaxation experiments. J Rheol 33:69–91CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Mataz Alcoutlabi
    • 1
  • S. G. Baek
    • 2
  • J. J. Magda
    • 1
    Email author
  • Xiangfu Shi
    • 3
  • S. A. Hutcheson
    • 3
  • G. B. McKenna
    • 3
  1. 1.Department of Materials Science and EngineeringUniversity of UtahSalt Lake CityUSA
  2. 2.RheoSense Inc.San RamonUSA
  3. 3.Department of Chemical EngineeringTexas Tech UniversityLubbockUSA

Personalised recommendations