An intriguing empirical rule for computing the first normal stress difference from steady shear viscosity data for concentrated polymer solutions and melts

Rheologica Acta

Volumn 51, Issue 6, 2012, Pages 487-495

  Sharma, Vivek ^a   McKinley, Gareth H ^a  

^a Massachusetts Institute of Technology Cambridge   (United States)

Author keywords

Cox Merz rule; First normal stress difference; Nonlinear viscoelasticity; Normal stresses; Shear viscosity; Third order fluid

Indexed keywords

EID: 84861602777     PISSN: 00354511     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00397-011-0612-8     Document Type: Article

References (44)

1. Al-Hadithi TSR, Barnes HA, Walters K (1992) The relationship between the linear (oscillatory) and nonlinear (steady-state) flow properties of a series of polymer and colloidal systems. Colloid Polym Sci 270: 40-46. doi: 10. 1007/bf00656927.
2. Annable T, Buscall R, Ettelaie R, Whittlestone D (1993) The rheology of solutions of associating polymers: comparison of experimental behavior with transient network theory. J Rheol 37: 695-726.
3. Barnes HA, Hutton JF, Walters K (1989) An introduction to rheology. Elsevier, Amsterdam.
4. Bird RB, Armstrong RC, Hassager O (1987) Dynamics of polymeric liquids. Wiley, New York.
5. Boger DV (1977) Highly elastic constant viscosity fluid. J Non-Newton Fluid Mech 3: 87-91. doi: 10. 1016/0377-0257(77)80014-1.
6. Booij HC, Leblans P, Palmen J, Tiemersmathoone G (1983) Nonlinear viscoelasticity and the Cox-Merz relations for polymeric fluids. J Polym Sci B Polym Phys 21: 1703-1711. doi: 10. 1002/pol. 1983. 180210910.
7. Cox WP, Merz EH (1958) Correlation of dynamic and steady flow viscosities. J Polym Sci 28: 619-622. doi: 10. 1002/pol. 1958. 1202811812.
8. Cross MM (1965) Rheology of non-Newtonian fluids-a new flow equation for pseudoplastic systems. J Colloid Sci 20: 417-437. doi: 10. 1016/0095-8522(65)90022-x.
9. Cross MM (1979) Relation between viscoelasticity and shear thinning behavior in liquids. Rheol Acta 18: 609-614. doi: 10. 1007/bf01520357.
10. Dealy JM, Larson RG (2006) Structure and rheology of molten polymers. Gardner, Cincinnati.
11. Dewitt TW (1955) A rheological equation of state which predicts non-Newtonian viscosity, normal stresses, and dynamic moduli. J Appl Phys 26: 889-894. doi: 10. 1063/1. 1722114.
12. DeWitt TW, Markovitz H, Padden FJ, Zapas LJ (1955) Concentration dependence of the rheological behavior of the polyisobutylene-decalin system. J Colloid Sci 10: 174-188.
13. Doi M, Edwards SF (1986) The theory of polymer dynamics. Oxford University Press, New York.
14. Doraiswamy D, Mujumdar AN, Tsao I, Beris AN, Danforth SC, Metzner AB (1991) The Cox-Merz rule extended: a rheological model for concentrated suspensions and other materials with yield stress. J Rheol 35: 647-685. doi: 10. 1122/1. 550184.
15. Ferry JD (1980) Viscoelastic properties of polymers. Wiley, New York.
16. Gemant A (1935) The conception of a complex viscosity and its application to dielectrics. Trans Faraday Soc 31: 1582-1589. doi: 10. 1039/tf9353101582.
17. Giacomin AJ, Bird RB, Johnson LM, Mix AW (2011) Large-amplitude oscillatory shear flow from the corotational Maxwell model. J Non-Newton Fluid Mech. doi: 10. 10116/j. jnnfm. 2011. 04. 002.
18. Gleissle W, Hochstein B (2003) Validity of the Cox-Merz rule for concentrated suspensions. J Rheol 47: 897-910. doi: 10. 1122/1. 1574020.
19. Harris J (1973) The Karl Weissenberg 80th birthday celebration essays. East African Literature Bureau, Kampala.
20. Ianniruberto G, Marrucci G (1996) On compatibility of the Cox-Merz rule with the model of Doi and Edwards. J Non-Newton Fluid Mech 65: 241-246. doi: 10. 1016/0377-0257(96)01433-4.
21. Kulicke WM, Porter RS (1980) Relation between steady shear flow and dynamic rheology. Rheol Acta 19: 601-605. doi: 10. 1007/bf01517513.
22. Lapasin R, Pricl S (1995) Rheology of industrial polysaccharides: theory and applications. Chapman & Hall, London.
23. Larson RG (1988) Constitutive equations for polymer solutions and melts. Butterworth, Boston.
24. Larson RG (1992) Instabilities in viscoelastic flows. Rheol Acta 31: 213-263. doi: 10. 1007/bf00366504.
25. Larson RG (1999) The structure and rheology of complex fluids. Oxford University Press, New York.
26. Laun HM (1986) Prediction of elastic strains of polymer melts in shear and elongation. J Rheol 30: 459-501. doi: 10. 1122/1. 549855.
27. Laun HM, Wagner MH, Janeschitz-Kriegl H (1979) Model analysis of nonlinear viscoelastic behavior by use of a single integral constitutive equation: stresses and birefringence of a polystyrene melt in intermittent shear flows. Rheol Acta 18: 615-622. doi: 10. 1007/bf01520358.
28. Lodge AS, Al-Hadithi TSR, Walters K (1987) Measurement of the 1st normal stress difference at high shear rates for a polyisobutadience decalin solution D2. Rheol Acta 26: 516-521. doi: 10. 1007/bf01333735.
29. Macosko CW (1994) Rheology: principles, measurements and applications. VCH, New York.
30. Markovitz H (1975) Superposition in rheology. J Polym Sci C Polym Symp 50: 431-456.
31. Marrucci G (1996) Dynamics of entanglements: a nonlinear model consistent with the Cox-Merz rule. J Non-Newton Fluid Mech 62: 279-289. doi: 10. 1016/0377-0257(95)01407-1.
32. Mead DW (2011) Analytic derivation of the Cox-Merz rule using the MLD "toy" model for polydisperse linear polymers. Rheol Acta. doi: 10. 1007/s00397-011-0550-5.
33. Milner ST (1996) Relating the shear-thinning curve to the molecular weight distribution in linear polymer melts. J Rheol 40: 303-315. doi: 10. 1122/1. 550742.
34. Mujumdar A, Beris AN, Metzner AB (2002) Transient phenomena in thixotropic systems. J Non-Newton Fluid Mech 102: 157-178. doi: 10. 1016/s0377-0257(01)00176-8.
35. Padden FJ, Dewitt TW (1954) Some rheological properties of concentrated polyisobutylene solutions. J Appl Phys 25: 1086-1091. doi: 10. 1063/1. 1721819.
36. Raghavan SR, Khan SA (1997) Shear-thickening response of fumed silica suspensions under steady and oscillatory shear. J Colloid Interface Sci 185: 57-67.
37. Renardy M (1997) Qualitative correlation between viscometric and linear viscoelastic functions. J Non-Newton Fluid Mech 68: 133-135. doi: 10. 1016/s0377-0257(96)01466-8.
38. Stastna J, De Kee D (1982) On the prediction of the primary normal stress coefficient from shear viscosity. J Rheol 26: 565-570. doi: 10. 1122/1. 549678.
39. Venkatraman S, Okano M, Nixon A (1990) A comparison of torsional and capillary rheometry for polymer melts: the Cox-Merz rule revisited. Polym Eng Sci 30: 308-313. doi: 10. 1002/pen. 760300508.
40. Wagner MH (1977) Prediction of primary normal stress difference from shear viscosity data using a single integral constitutive equation. Rheol Acta 16: 43-50. doi: 10. 1007/bf01516928.
41. Walters K (1975) Rheometry. Chapman Hall, London.
42. Weissenberg K (1947) A continuum theory of rheological phenomena. Nature 159: 310-311. doi: 10. 1038/159310a0.
43. Winter HH (2009) Three views of viscoelasticity for Cox-Merz materials. Rheol Acta 48: 241-243. doi: 10. 1007/s00397-008-0329-5.
44. Yasuda K, Armstrong RC, Cohen RE (1981) Shear flow properties of concentrated solutions of linear and star branched polystyrenes. Rheol Acta 20: 163-178. doi: 10. 1007/bf01513059.