Normal stress differences in large-amplitude oscillatory shear flow for the corotational "ANSR" model

Rheologica Acta

Volumn 50, Issue 9-10, 2011, Pages 741-752

  Giacomin, Alan Jeffrey ^a   Bird, Robert Byron ^a  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

Corotating frame; Normal stresses; Oscillatory flow; Second normal stress difference

Indexed keywords

EID: 80052038812     PISSN: 00354511     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00397-011-0553-2     Document Type: Article

References (46)

1. Abdel-Khalik SI, Hassager O, Bird RB (1974) The Goddard expansion and the kinetic theory for solutions of rodlike macromolecules. J Chem Phys 61: 4312-4316.
2. Andrä R, Spurk JH (1982) Complex viscosity of viscoelastic damping fluids. Rheol Acta 21: 530-533.
3. 22 in Eq. (12. 9), 1/120 should be 1/280; in lines 3 and 4 from below, ∂/∂t should be d/dt; Eqs. 25. 20 to 25-22 were given earlier (Giesekus 1962); in Acknowledgements, "Frant" should be "Grant," and "OH Christiansen" is now "Ole Hassager".
4. Bird RB, Hassager O, Abdel-Khalik SI (1974) Co-rotational rheological models and the Goddard expansion. AIChE J 20: 1041-1066.
5. Bird RB, Armstrong RC, Hassager O (1977) Dynamics of polymeric liquids, vol 1, 1st edn. Wiley, New York.
6. Bird RB, Stewart WE, Lightfoot EN (2007) Transport phenomena, revised 2nd edn. Wiley, New York.
7. Böhme G (1981) Strömungsmechanik nicht-newtonscher Fluide. BG Teubner, Stuttgart.
8. Christiansen EB, Leppard WR (1974) Steady-state and oscillatory flow properties of polymer solutions. Trans Soc Rheol 18: 65-86.
9. Endo H, Nagasawa M (1970) Normal stress and shear stress in a viscoelastic liquid under oscillatory shear flow. J Polym Sci: Part A-2 8: 371-381.
10. Férec J, Heuzey MC, Ausias G, Carreau PJ (2008) First normal stress difference of entangled polymer solutions in large amplitude oscillatory shear flow. J Non-Newton Fluid Mech 151: 89-100.
11. Gao HW (1979) The effect of the molecular weight and molecular weight distribution on the viscoelastic flow functions of linear polystyrene solutions. PhD Thesis, University of Utah, Dept of Chemical Engineering, Salt Lake City, UT.
12. Gao HW, Ramachandran S, Christiansen EB (1974) Dependency of the steady-state and transient viscosity and first and second normal stress difference functions on molecular weight for linear mono and polydisperse polystyrene solutions. Trans Soc Rheol 18: 65-86.
13. Gao HW, Ramachandran S, Christiansen EB (1981) Dependency of the steady-state and transient viscosity and first and second normal stress difference functions on molecular weight for linear mono and polydisperse polystyrene solutions. J Rheol 25: 213-235.
14. Georgian JC (1949) Torsional viscous friction dampers. Trans Am Soc Mech Eng 71: 389-399.
15. Giacomin AJ, Bird RB, Johnson LM, Mix AW (2010) Large-amplitude oscillatory shear flow from the corotational Maxwell model. Rheology Research Center Report No 187, University of Wisconsin, Madison, WI.
16. Giacomin AJ, Bird RB, Johnson LM, Mix AW (2011) Large-amplitude oscillatory shear flow from the corotational Maxwell model. J Non-Newton Fluid Mech 166 (in press).
17. Giesekus H (1962) Elasto-viskose Flüssigkeiten, für die in stationären Schichtströmungen sämtliche Normalspannungskomponenten verschieden groß sind. Rheol Acta 2: 50-62.
18. Hagner KE, Maass H (1985) Torsionsschwingungen in der Verbrennungskraftmaschine. Springer, Vienna.
19. Kannan RM (1992) Flow-induced alignment in intrinsically anisotropic polymeric materials. PhD Thesis, California Institute of Technology, Dept of Chemical Engineering, Pasadena, CA.
20. Kannan RM, Kornfield JA (1992) The third-normal stress difference in entangled melts: quantitative stress-optical measurements in oscillatory shear. Rheol Acta 31: 535-544.
21. Keentok M, Xue SC (1999) Edge fracture in cone-plate and parallel plate flows. Rheol Acta 38: 321-348.
22. Kornfield JA, Fuller GG, Pearson DS (1991) Third normal stress difference and component relaxation spectra for bidisperse melts under oscillatory shear. Macromolecules 24: 5429-5441.
23. Labiausse V, Höhler R, Cohen-Addad S (2007) Shear induced normal stress differences in aqueous foams. J Rheol 51: 479-492.
24. 2 control the onset of edge fracture? Rheol Acta 31: 306-308.
25. Leppard WR (1975) Viscoelasticity: stress measurements and constitutive theory. PhD Thesis, University of Utah, Dept of Chemical Engineering, Salt Lake City, UT.
26. Nam JG, Anh KH, Lee SJ (2008) Prediction of normal stresses under large amplitude oscillatory shear flow. J Non-Newton Fluid Mech 150: 1-10.
27. Nam JG, Hyun K, Anh KH, Lee SJ (2008) Analysis of the normal stress differences of viscoelastic fluids under large amplitude oscillatory shear flow. In: Co A, Leal LG, Colby RH, Giacomin AJ (eds) Proceedings, The XVth International Congress on Rheology, The Society of Rheology 80Th Annual Meeting, pp 171-173.
28. Nam JG, Hyun K, Anh KH, Lee SJ (2010) First normal stress difference of entangled polymer solutions in large amplitude oscillatory shear flow. J Rheol 54: 1243-1266.
29. Nestorides EJ (1958) A handbook on torsional vibration. Cambridge University Press, Cambridge.
30. Oakley JG (1992) Measurement of normal thrust and evaluation of upper-convected Maxwell models in large amplitude oscillatory shear. Masters Thesis, Texas A&M University, Mechanical Engineering Dept, College Station, TX.
31. Oakley JG, Giacomin AJ (1994) A sliding plate normal thrust rheometer for molten plastics. Polym Eng Sci 34: 580-584.
32. -iωs in Eq. (A2); after Eq. (A. 10), α should be, and in Eq. (A. 11), cosx should be coshx.
33. Reimers MJ (1996) Sliding plate rheometer studies of concentrated polystyrene solutions. PhD Thesis, McGill University, Dept of Chemical Engineering, Montreal, Canada.
34. Reimers MJ, Dealy JM (1996) Sliding plate rheometer studies of concentrated polystyrene solutions: large amplitude oscillatory shear of a very high molecular weight polymer in diethyl phthalate. J Rheol 40: 167-186.
35. Reimers MJ, Dealy JM (1998) Sliding plate rheometer studies of concentrated polystyrene solutions: nonlinear viscoelasticity and wall slip of two high molecular weight polymers in tricresyl phosphate. J Rheol 42: 527-548.
36. Schultz K (1978) Ermittlung des physikalischen Verhaltens von hochviskosen Flüssigkeiten bei harmonsischer Schubwechselbeanspruchung. Rheol Acta 17: 33-41.
37. Spriggs TW (1965) A four-constant model for viscoelastic fluids. Chem Eng Sci 20: 931-940.
38. Spriggs TW (1966) Constitutive equations for viscoelastic fluids. PhD Thesis, Chemical Engineering Department, University of Wisconsin, Madison, WI.
39. Tadmor Z, Bird RB (1974) Rheological analysis of stabilizing forces in wire-coating dies. Polym Eng Sci 14: 124-136.
40. Tanner RI, Keentok M (1983) Shear fracture in cone plate rheometry. J Rheol 27: 47-57.
41. Venerus DC (1989) Rheological constitutive equation development and evaluation for viscoelastic liquids. PhD Thesis, The Pennsylvania State University, University Park, PA.
42. Vrentas JS, Venerus DC, Vrentas CM (1991) Finite amplitude oscillations of viscoelastic fluids. J Non-Newton Fluid Mech 40: 1-24.
43. Wada E (1953) Non-Newtonian viscosity of dilute high polymer solution. II. Effects of concentration, temperature and degree of polymerization; method of measuring true intrinsic viscosity. J Sci Res Inst 47: 168-170.
44. Wakabayashi K, Honda Y, Kodama T, Iwamoto S (1992) The dynamic characteristics of torsional viscous-friction dampers on reciprocating engine shaftings. SAE Technical Paper Series, 921726, SAE International, International Off-Highway & Powerplant Congress & Exhibition, Milwaukee, WI (14-17 September 1992), pp 1-21.
45. Xu J (2005) Nonlinear viscoelasticity and wall slip of molten polymers. MEng Thesis, Dept of Chemical Engineering, McGill University, Montreal, Canada.
46. Xu J, Costeux S, Dealy JM, De Decker MN (2007) Use of a sliding plate rheometer to measure the first normal stress difference at high shear rates. Rheol Acta 46: 815-824.