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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access May 30, 2019

On numerical Simulations of Polymer Extrusion Instabilities

  • Evdokia Achilleos , Georgios C. Georgiou EMAIL logo and Savvas G. Hatzikiriakos
From the journal Applied Rheology

Abstract

The objective of this study is mainly to review recent work concerning the numerical modeling of the stick-slip and gross melt fracture polymer extrusion instabilities. Three different mechanisms of instability are discussed: (a) combination of nonlinear slip with compressibility; (b) combination of nonlinear slip with elasticity; and (c) constitutive instabilities. Furthermore, preliminary numerical simulations of the time-dependent, compressible extrudate-swell flow of a Carreau fluid with slip at the wall, using a realistic macroscopic slip equation that is based on experimental data for a high-density polyethylene, are presented.

REFERENCES

[1] Petrie CJS, Denn MM: Instabilities in Polymer Processing, AIChE J. 22 (1976) 209-236.Search in Google Scholar

[2] Denn MM: Issues in Viscoelastic Fluid Mechanics, Annu. Rev. Fluid Mech. 22 (1990) 13-34.10.1146/annurev.fl.22.010190.000305Search in Google Scholar

[3] Denn MM: Extrusion Instabilities and Wall Slip, Annu. Rev. Fluid Mech. 33 (2001) 265-287.10.1146/annurev.fluid.33.1.265Search in Google Scholar

[4] Larson RG: Instabilities in Viscoelastic Flows, Rheol. Acta 31 (1992) 213-263.10.1007/BF00366504Search in Google Scholar

[5] Leonov AI, Prokunin AN: Nonlinear Phenomena in Flows of Viscoelastic Polymer Fluids, Chapman and Hall, London (1994).Search in Google Scholar

[6] Piau JM, El Kissi N, Toussaint F, Mezghani A: Distortions of Polymer Melt Extrudates and their Elimination using Slippery Surfaces, Rheol. Acta 34 (1995) 40-57.Search in Google Scholar

[7] El Kissi N, Piau JM: Stability Phenomena during Polymer Melt Extrusion, in Rheology for Polymer Melt Processing, Piau JM, Agassant JF (Eds.), Elsevier Science, New York (1996) 389-420.10.1016/S0169-3107(96)80014-1Search in Google Scholar

[8] Wang SQ: Molecular Transitions and Dynamics at Polymer/Wall Interfaces: Origins of Flow Instabilities and Wall Slip, Adv. Polym. Sci. 138 (1999) 227-275.Search in Google Scholar

[9] Adewale KEP, Leonov AI: Modeling Spurt and Stress Oscillations in Flows of Molten Polymers, Rheol. Acta 36 (1997) 110-127.Search in Google Scholar

[10] Ramamurthy AV: Wall Slip in Viscous Fluids and Influence of Materials of Construction, J. Rheol. 30 (1986) 337-357.Search in Google Scholar

[11] Kalika DS, Denn MM: Wall Slip and Extrudate Distortion in Linear Low-Density Polyethylene, J. Rheol. 31 (1987) 815-834.10.1122/1.549942Search in Google Scholar

[12] Piau JM, El Kissi N, Tremblay B: Influence of Upstream Instabilities and Wall Slip on Melt Fracture and Sharkskin Phenomena during Silicones Extrusion through Orifice Dies, J. Non-Newtonian Fluid Mech. 34 (1990) 145-180.Search in Google Scholar

[13] Hatzikiriakos SG, Dealy JM: Role of Slip and Fracture in the Oscillating Flow of HDPE in a Capillary, J. Rheol. 36 (1992) 845-884.10.1122/1.550320Search in Google Scholar

[14] El Kissi N, Piau JM: Stability Phenomena during Polymer Melt Extrusion, J. Rheol. 38 (1994) 1447-1463.Search in Google Scholar

[15] El Kissi N, Piau JM, Toussaint F: Sharkskin and Cracking of Polymer Melt Extrudates, J. Non-Newtonian Fluid Mech. 68 (1997) 271-290.10.1016/S0377-0257(96)01507-8Search in Google Scholar

[16] De Kee D, Wissbrun KF: Polymer Rheology, Physics Today 51 (1998) 24-29.Search in Google Scholar

[17] Hill DA, Hasegawa T, Denn MM: On the Apparent Relation between Adhesive Failure and Melt Fracture, J. Rheol. 34 (1990) 891-918.10.1122/1.550105Search in Google Scholar

[18] Hatzikiriakos SG, Dealy JM: Wall Slip of Molten High Density Polyethylenes. II. Capillary Rheometer Studies, J. Rheol. 36 (1992) 703-741.10.1122/1.550313Search in Google Scholar

[19] Mackay ME, Henson DJ: The Effect of Molecular Mass and Temperature on the Slip of Polystyrene Melts at Low Stress Levels, J. Rheol. 42 (1998) 1505-1517.10.1122/1.550930Search in Google Scholar

[20] Wise GM, Denn MM, Bell AT, Mays JW, Hong K, Iatrou H: Surface Mobility and Slip of Polybutadiene Melts in Shear Flow, J. Rheol. 44 (2000) 549-567.10.1122/1.551100Search in Google Scholar

[21] Inn YW, Fischer RJ, Shaw MT: Visual Observation of Development of Sharkskin Melt Fracture in Polybutadiene Extrusion, Rheol. Acta 37 (1998) 573-582.Search in Google Scholar

[22] Ghanta VG, Riise BL, Denn MM: Disappearance of Extrusion Instabilities in Brass Capillary Dies, J. Rheol. 43 (1999) 435-442.10.1122/1.550988Search in Google Scholar

[23] Amos SE, Giacoletto GM, Horns JH, Lavallée C, Woods SS: Polymer Processing Aids (PPA), in Plastic Additives, Hanser, New York (2001) 553-584.Search in Google Scholar

[24] Migler KB, Lavallée C, Dillon MP, Woods SS, Gettinger CL: Visualizing the Elimination of Shark-skin through Fluoropolymer Additives: Coating and Polymer-Polymer Slippage, J. Rheol. 45 (2001) 565-581.Search in Google Scholar

[25] Achilleos E, Georgiou G, Hatzikiriakos SG: The Role of Processing Aids in the Extrusion of Polymer Melts, J. Vinyl & Additive Technology 8 (2000) 7-24.10.1002/vnl.10340Search in Google Scholar

[26] Fyrillas MM, Georgiou GC, Vlassopoulos D, Hatzikiriakos SG: A Mechanism for Extrusion Instabilities in Polymer Melts, Polymer Eng. Sci. 39 (1999) 2498-2504.Search in Google Scholar

[27] Münstedt H, Schmidt M, Wassner E: Stick and Slip Phenomena during Extrusion of Polyethylene Melts as Investigated by Laser-Doppler Velocimetry, J. Rheol. 44 (2000) 413-427.10.1122/1.551092Search in Google Scholar

[28] Tanner RI, Walters K: Rheology: An Historical Perspective, Elsevier, Amsterdam (1998).Search in Google Scholar

[29] Liang Y, Oztekin A, Neti S: Dynamics of Viscoelastic Jets of Polymeric Liquid Extrudate, J. Non-Newtonian Fluid Mech. 81 (1999) 105-132.10.1016/S0377-0257(98)00093-7Search in Google Scholar

[30] Li H, Hürlimann HP, Meissner J: Two Separate Ranges for Shear Flow Instabilities with Pressure Oscillations in Capillary Extrusion of HDPE and LLDPE, Polym. Bull. 15 (1986) 83-88.Search in Google Scholar

[31] Robert L, Vergnes B, Demay Y: Complex Transients in the Capillary Flow of Linear Polyethylene, J. Rheol. 44 (2001) 1183-1187.Search in Google Scholar

[32] Fernández M, Santamaria A, Muñoz-Escalona A, Méndez L: A Striking Hydrodynamic Phenomenon: Split of a Polymer Melt in Capillary Flow, J. Rheol. 45 (2001) 595-602.10.1122/1.1346600Search in Google Scholar

[33] Cogswell FN: Stretching Flow Instabilities at the Exits of Extrusion Dies, J. Non-Newtonian Fluid Mech. 2 (1977) 37-57.10.1016/0377-0257(77)80031-1Search in Google Scholar

[34] Barone JR, Wang SQ: Rheo-optical Observations of Sharkskin Formation in Slit-Die Extrusion, J. Rheol. 45 (2001) 49-60.10.1122/1.1332385Search in Google Scholar

[35] Pérez-González J, Pérez-Trejo L, de Vargas L, Manero O: Inlet Instabilities in the Capillary Flow of Polyethylene Melts, Rheol. Acta 36 (1997) 677-685.Search in Google Scholar

[36] Piau JM, Nigen S, El Kissi N: Effect of Die Entrance Filtering on Mitigation of Upstream Instability during Extrusion of Polymer Melts, J. Non-Newtonian Fluid Mech. 91 (2000) 37-57.Search in Google Scholar

[37] Migler KB, Son Y, Qiao F, Flynn K: Extensional Deformation, Cohesive Failure, and Boundary Conditions During Sharkskin Melt Fracture, J. Rheol. 46 (2002) 383-400.Search in Google Scholar

[38] Joseph DD, Joe Liu Y: Letter to the Editor: Steep Wave Fronts on Extrudates of Polymer Melts and Solutions, J. Rheol. 40 (1996) 317-319.10.1122/1.550743Search in Google Scholar

[39] Kurtz SJ: Comment to the Editor, J. Rheol. 40 (1996) 319-320.10.1122/1.550744Search in Google Scholar

[40] Graham MD: The Sharkskin Instability of Polymer Melt Flows, Chaos 9 (1999) 154-163.10.1063/1.166386Search in Google Scholar PubMed

[41] Venet C, Vergnes B: Stress Distribution around Capillary Die Exit: an Interpretation of the Onset of Sharkskin Effect, J. Non-Newtonian Fluid Mech. 93 (2000) 117-132.Search in Google Scholar

[42] Rutgers R., Mackley M: The Correlation of Experimental Surface Extrusion Instabilities with Numerically Predicted Exit Surface Stress Concentrations and Melt Strength for Linear Low Density Polyethylene, J. Rheol. 44 (2000) 1319-1334.10.1122/1.1319176Search in Google Scholar

[43] Demarquette NR, Dealy JM: Nonlinear Viscoelasticity of Concentrated Polystyrene Solutions: Sliding Plate Rheometer Studies, J. Rheol. 36 (1992) 1007-1032.10.1122/1.550299Search in Google Scholar

[44] Chen YL, Larson RG, Patel SS: Shear Fracture of Polystyrene Melts and Solutions, Rheol. Acta 33 (1994) 243-257.Search in Google Scholar

[45] Mhetar V, Archer LA: Slip in Entangled Polymer Solutions, Macromolecules 31 (1998) 6639-6649.10.1021/ma971339hSearch in Google Scholar

[46] Joshi YM, Lele AK, Mashelkar RA: Slipping Fluids: A Unified Transient Network Model, J. Non-Newtonian Fluid Mech. 89 (2000) 303-355.Search in Google Scholar

[47] Barone JR, Plucktaveesak N, Wang SQ: Interfacial Molecular Instability Mechanism for Sharkskin Phenomenon in Capillary Extrusion of Linear Polyethylenes, J. Rheol. 42 (1992) 813-832.Search in Google Scholar

[48] Wang SQ, Drda PA: Superfluid-like Stick-Slip Transition in Capillary Flow of Linear Polyethylene. 1. General Features, Macromolecules 29 (1996) 2627-2632.10.1021/ma950898qSearch in Google Scholar

[49] Wang SQ, Drda PA: Superfluid-like Stick-Slip Transition in Capillary Flow of Linear Polyethylene. 2. Molecular Weight and Low-Temperature Anomaly, Macromolecules 29 (1996) 4115-4119.Search in Google Scholar

[50] Wang SQ, Drda PA: Stick-Slip Transition in Capillary Flow of Linear Polyethylene. 3. Surface Conditions, Rheol. Acta 36 (1997) 128-134.Search in Google Scholar

[51] Hatzikiriakos SG, Dealy JM: Wall Slip of Molten High Density Polyethylenes. I. Sliding Plate Rheometer Studies, J. Rheol. 35 (1991) 495-523.Search in Google Scholar

[52] Reimers MJ, Dealy JM: 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 (1996) 167-186.10.1122/1.550738Search in Google Scholar

[53] Reimers MJ, Dealy JM: 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 (1998) 527-548.Search in Google Scholar

[54] Koran F, Dealy JM: Wall Slip of Polyisobutylene: Interfacial and Pressure Effects, J. Rheol. 43 (1999) 1291-1306.Search in Google Scholar

[55] Awati KM, Park Y, Wisser E, Mackay ME: Wall Slip and Shear Stresses of Polymer Melts at High Shear Rates without Pressure and Viscous Heating Effects, J. Non-Newtonian Fluid Mech. 89 (2000) 117-131.Search in Google Scholar

[56] Migler KB, Hervet H, Leger L: Slip Transition of a Polymer Melt under Shear Stress, Phys. Rev. Lett. 70 (1993) 287-290.10.1103/PhysRevLett.70.287Search in Google Scholar PubMed

[57] Durliat E, Hervet H, Leger L: Influence of Grafting Density on Wall Slip of a Polymer Melt on a Polymer Brush, Europhys. Lett. 38 (1997) 383-388.Search in Google Scholar

[58] Archer LA, Larson RG, Chen YL: Direct Measurements of Slip in Sheared Polymer Solutions, J. Fluid Mech. 301 (1995) 133-151.Search in Google Scholar

[59] Legrand F, Piau JM: Wall Slip of a Polydimethylsiloxane Extruded through a Slit Die with Rough Steel Surfaces: Micrometric Measurement at the Wall with Fluorescent-Labeled Chains, J. Rheol. 42 (2000) 1389-1402.Search in Google Scholar

[60] Hatzikiriakos SG: A Slip Model for Linear Polymers Based on Adhesive Failure, Intern. Polymer Processing VIII(2) (1993) 135-142.Search in Google Scholar

[61] De Gennes PG: “Mécaniques des Fluides: Écoulements Viscométriques de Polymères Enchevêtrés”, C.R. Acad. Sci. Paris 288 (1979) 219-220.Search in Google Scholar

[62] De Gennes PG: Wetting: Statics and Dynamics, Rev. Modern Phys. 57 (1985) 827-863.10.1103/RevModPhys.57.827Search in Google Scholar

[63] Brochard F, de Gennes PG: Shear-Dependent Slippage at a Polymer/Solid Interface, Langmuir 8 (1992) 3033-3037.Search in Google Scholar

[64] Ajdari A, Brochard-Wyart F, de Gennes PG, Leibler L, Viory LL, Rubinstein M: Slippage of an Entangled Polymer Melt on a Grafted Surface, Physica A 204 (1994) 17-39.Search in Google Scholar

[65] Brochard-Wyart F, Gay C, de Gennes PG: Slippage of Polymer Melts on Grafted Surfaces, Macromolecules 29 (1996) 377-382.10.1021/ma950753jSearch in Google Scholar

[66] Drda PA, Wang SQ: Stick-Slip Transition at Polymer Melt/Solid Interfaces, Phys. Rev. Let. 75 (1995) 2698-2701.10.1103/PhysRevLett.75.2698Search in Google Scholar PubMed

67] Lau HC, Schowalter WR: A Model for Adhesive Failure of Viscoelastic Fluids during Flow, J. Rheol. 30 (1986) 193-206.10.1122/1.549888Search in Google Scholar

[68] Denn MM: Surface-Induced Effects in Polymer Melt Flow, in Theoretical and Applied Rheology, Moldenaers P, Keunings R (Eds.), Elsevier Science Publishers (1992) 45-49.10.1016/B978-0-444-89007-8.50014-9Search in Google Scholar

[69] Stewart CW: Wall Slip in the Extrusion of Linear Polyolefins, J. Rheol. 37 (1993) 499-512.Search in Google Scholar

[70] El Kissi N, Piau JM: Écoulement de Fluides Polymères Enchevêtrés dans un Capillaire. Modélisation du Glissement Macroscopique á la Paroi, C. R. Acad. Sci. Paris 309, Série II (1989) 7-9.Search in Google Scholar

[71] Leonov AI: On the Dependence of Friction Force on Sliding Velocity in the Theory of Adhesive Friction of Elastomers, Wear 141 (1990) 137-145.Search in Google Scholar

[72] Yarin AL, Graham MD: A Model for Slip at Polymer/Solid Interfaces, J. Rheol. 42 (1998) 1491-1503.Search in Google Scholar

[73] Wang SQ, Drda PA, Inn YW: Exploring Molecular Origins of Sharkskin, Partial Slip, and Slope Change in Flow Curves of Linear Density Polyethylene, J. Rheol. 40 (1996) 875-897.Search in Google Scholar

[74 Hill DA: Wall-Slip in Polymer Melts: A Pseudo-chemical Model, J. Rheol. 42 (1998) 581-601.10.1122/1.550901Search in Google Scholar

[75] Black WB, Graham MD: Wall-Slip and Polymer Melt Flow Instability, Phys. Rev. Lett. 77 (1996) 956-959.Search in Google Scholar

[76] Black WB, Graham MD: Effect of Wall Slip on the Stability of Viscoelastic Plane Shear Flow, Phys. Fluids 11 (1999) 1749-1756.10.1063/1.870040Search in Google Scholar

[77] Black WB: Wall Slip and Boundary Effects in Polymer Shear Flows, Ph.D. Thesis, Department of Chemical Engineering, University of Wisconsin -Madison (2000).Search in Google Scholar

[78] Pearson JRA, Petrie CJS: On the Melt-Flow Instability of Extruded Polymers, Proc. 4th Int. Rheo-logical Congress 3 (1965) 265-282.Search in Google Scholar

[79] Georgiou GC: On the Stability of the Shear Flow of a Viscoelastic Fluid with Slip along the Fixed Wall, Rheol. Acta 35 (1996) 39-47.Search in Google Scholar

[80] Fyrillas M, Georgiou GC: Linear Stability Diagrams of the Shear Flow of an Oldroyd-B Fluid with Slip along the Fixed Wall, Rheol. Acta 37 (1998) 61-67.Search in Google Scholar

[81] Brasseur E, Fyrillas MM, Georgiou GC, Crochet MJ: The Time-Dependent Extrudate-Swell Problem of an Oldroyd-B Fluid with Slip along the Wall, J. Rheol. 42 (1998) 549-566.10.1122/1.550959Search in Google Scholar

[82] Shore JD, Ronis D, Piché L, Grant M: Model for Melt Fracture Instabilities in the Capillary Flow of Polymer Melts, Phys. Rev. Let. 77 (1996) 655-658.Search in Google Scholar

[83] Shore JD, Ronis D, Piché L, Grant M: Theory of Melt Fracture Instabilities in the Capillary Flow of Polymer Melts, Phys. Rev. E 55 (1997) 2976-2992.Search in Google Scholar

[84] Shore JD, Ronis D, Piché L, Grant M: Sharkskin Texturing Instabilities in the Flow of Polymer Melts, Physica A 239 (1997) 350-357.Search in Google Scholar

[85] Pearson JRA: Mechanics of Polymer Processing, Elsevier, London (1985).Search in Google Scholar

[86] Georgiou GC, Crochet MJ: Compressible Viscous Flow in Slits, with Slip at the Wall, J. Rheol. 38 (1994) 639-654.10.1122/1.550479Search in Google Scholar

[87] Georgiou GC, Crochet MJ: Time-Dependent Compressible Extrudate-Swell Problem with Slip at the Wall, J. Rheol. 38 (1994) 1745-1755.Search in Google Scholar

[88] Georgiou GC: Extrusion of a Compressible Newtonian Fluid with Periodic Inflow and Slip at the Wall, Rheol. Acta 35 (1996) 531-544.Search in Google Scholar

[89] Den Doelder CFJ, Koopmans RJ, Molenaar J, Van de Ven AAF: Comparing the Wall Slip and the Constitutive Approach for Modelling Spurt Instabilities in Polymer Melt Flows, J. Non-Newtonian Fluid Mech. 75 (1998) 25-41.Search in Google Scholar

[90] Ranganathan M, Mackley MR, Spitteler PHJ: The Application of the Multipass Rheometer to Time-Dependent Capillary Flow Measurements of a Polyethylene Melt, J. Rheol. 43 (1999) 443-451.10.1122/1.550990Search in Google Scholar

[91] Kumar KA, Graham MD: The Effect of Pressure-Dependent Slip on Flow Curve Multiplicity, Rheol. Acta 37 (1998) 245-255.Search in Google Scholar

[92] Yerushalmi J, Katz S, Shinnar R: The Stability of Steady Shear Flows of some Viscoelastic Fluids, Chem. Eng. Sci. 25 (1970) 1891-1902.10.1016/0009-2509(70)87007-5Search in Google Scholar

[93] McLeish TCB, Ball RC: A Molecular Approach to the Spurt Effect in Polymer Melt Flow, J. Polym. Sci. B24 (1986) 1735-1745.10.1002/polb.1986.090240809Search in Google Scholar

[94] Lin YH: Explanation for Stick-Slip Melt Fracture in Terms of Molecular Dynamics in Polymer Melts, J. Rheol. 29 (1985) 605-637.10.1122/1.549804Search in Google Scholar

[95] Kolkka RW, Malkus DS, Hansen MG, Ierley GR, Worthing RA: Spurt Phenomena of the Johnson-Segalman Fluid and Related Models, J. Non-Newtonian Fluid Mech. 29 (1988) 303-335.10.1016/0377-0257(88)85059-6Search in Google Scholar

[96] Vlassopoulos D, Hatzikiriakos SG: A Generalized Giesekus Constitutive Model with Retardation Time and its Association to the Spurt Effect, J. Non-Newtonian Fluid Mech. 57 (1995) 119-136.Search in Google Scholar

[97] Aarts K, Van de Ven AAF: Transient Behaviour and Stability Points of the Poiseuille Flow of a KBKZ-Fluid, J. Eng. Maths. 29 (1995) 371-392.Search in Google Scholar

[98] Decruppe JP, Cressely R, Makhloufi R, Cappelaere E: Flow Birefringence Experiments Showing a Shear-Banding Structure in a CTAB Solution, Colloid Polym. Sci. 273 (1995) 346-351.Search in Google Scholar

[99] Mair RW, Callaghan PT: Shear Flow of Wormlike Micelles in Pipe and Cylindrical Couette Geometries as Studied by Nuclear Magnetic Resonance Microscopy, J. Rheol. 41 (1997) 901-924.Search in Google Scholar

[100] Britton MM, Mair RW, Lambert RK, Callaghan PT: Transition to Shear Banding in Pipe and Couette Flow of Wormlike Micellar Solutions, J. Rheol. 43 (1999) 897-909.10.1122/1.551008Search in Google Scholar

[101] Callaghan PT, Cates ME, Rofe CJ, Smeulders JBAF: The Spurt Effect Observed in Wormlike Micelles Using Nuclear Magnetic Resonance Microscopy, J. Phys. II France 6 (1996) 375-393.Search in Google Scholar

[102] Hunter JK, Slemrod M: Viscoelastic Fluid Flow Exhibiting Hysteretic Phase Changes, Phys. Fluids 26 (1983) 2345-2351.10.1063/1.864437Search in Google Scholar

[103] Fyrillas M, Georgiou GC, Vlassopoulos D: Time-Dependent Plane Poiseuille Flow of a Johnson-Segalman Fluid, J. Non-Newtonian Fluid Mech. 82 (1999) 105-123.Search in Google Scholar

[104] Spenley NA, Yuan XF, Cates ME: Nonmonotonic Constitutive Laws and the Formation of Shear-Banded flows, J. Phys. II France 6 (1996) 551-571.Search in Google Scholar

[105] Malkus DS: Numerical Simulation of Shear-Flow Dynamics of Three Simple Flows using the Johnson-Segalman Model, RRC144, University of Wisconsin, Madison (1997).Search in Google Scholar

[106] Aarts ACT: Analysis of the Flow Instabilities in the Extrusion of Polymeric Melts, Ph.D. Thesis, Eindhoven University of Technology, The Netherlands (1997).Search in Google Scholar

[107] Yuan XF, Ball RC, Edwards SF: A New Approach to Modelling Viscoelastic Flow, J. Non-Newtonian Fluid Mech. 46 (1993) 331-350.10.1016/0377-0257(93)85054-ESearch in Google Scholar

[108] Georgiou GC, Vlassopoulos D: On the Stability of the Simple Shear Flow of a Johnson-Segalman Fluid, J. Non-Newtonian Fluid Mech. 75 (1998) 77-97.Search in Google Scholar

[109] Malkus DS, Nohel JA, Blohr BJ: Oscillation in Piston-Driven Shear Flow of a Non-Newtonian Fluid, in Numerical Simulation of Non-Isothermal Flow of Viscoelastic Liquids, Dijksamn JF, Kuiken GD (Eds.), Kluwer, Dordrecht (1993) 57-71.Search in Google Scholar

[110] Olmsted PD, Radulescu O: Johnson-Segalman Model with a Diffusion Term in Cylindrical Couette Flow, J. Rheol. 44 (2000) 257-275.Search in Google Scholar

[111] Yuan XF: Dynamics of Mechanical Interface in Shear-Banded Flow, Europhys. Lett. 46 (1999) 542-548.Search in Google Scholar

[112] Lu CYD, Olmsted PD, Ball RC: Effects of Nonlocal Stress on the Determination of Shear Banding Flow, Phys. Rev. Lett. 84 (2000) 642-645.Search in Google Scholar

[113] Español P, Yuan XF, Ball RC: Shear Banding Flow in a Johnson-Segalman Fluid, J. Non-Newtonian Fluid Mech. 65 (1996) 93-109.10.1016/0377-0257(96)01451-6Search in Google Scholar

[114] Greco F, Ball RC: Shear-Band Formation in a Non-Newtonian Fluid Model with a Constitutive Instability, J. Non-Newtonian Fluid Mech. 69 (1997) 195-206.Search in Google Scholar

[115] Ashrafi N, Khayat RE: A Low-Dimensional Approach to Nonlinear Plane-Couette Flow of Viscoelastic Fluids, Physics of Fluids 12 (2000) 345-365.10.1063/1.870313Search in Google Scholar

[116] Molenaar J, Koopmans RJ: Modelling Polymer Melt-Flow Instabilities, J. Rheol. 38 (1994) 99-109.Search in Google Scholar

[117] Wang SQ, Barone JR, Yang X, Deeprasertkul C, Plucktaveesak N, Chai CK, Capaccio G, Hope PS: Flow Instabilities in Polymer Processing: Past Controversies, Current Understanding, and Future Challenges, in Proceedings of the XIIIth International Congress on Rheology, Binding DM, Hudson NE, Mewis J, Piau JM, Petrie CJS, Townsend P, Wagner MH, Walters K (Eds.), Vol. 3 (2000) 164-166.Search in Google Scholar

[118] Lim FJ, Schowalter WR: Wall Slip of Narrow Molecular Weight Distribution Polybutadienes, J. Rheol. 33 (1989) 1359-1382.10.1122/1.550073Search in Google Scholar

[119] El Kissi N, Piau JM: The Different Capillary Flow Regimes of Entangled Polydimethylsiloxane Polymers: Macroscopic Slip at the Wall, Hysteresis and Cork Flow, J. Non-Newtonian Fluid Mech. 37 (1990) 55-94.Search in Google Scholar

[120] Adewale KEP, Leonov AI: On Modeling Spurt Flows of Polymers, J. Non-Newtonian Fluid Mech. 49 (1993) 133-138.10.1016/0377-0257(93)85027-8Search in Google Scholar

[121] Georgiou GC, Schultz WW, Olson LO: Singular Finite Elements for the Sudden-Expansion and the Die-Swell Problems, Int. J. Numer. Methods Fluids 10 (1990) 357-372.Search in Google Scholar

Received: 2001-11-22
Accepted: 2002-04-13
Published Online: 2019-05-30
Published in Print: 2002-04-01

© 2002 Evdokia Achilleos et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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