Numerical Simulations of BVPs and IVPs in Fiber Spinning Using Giesekus Constitutive Model in hpk Framework

REFERENCES

• Kase , S. and Matsuo , T. 1967 . Studies on Melt Spinning. II. Steady-state and Transient Solutions of Fundamental Equations Compared with Experimental Results . Journal of Applied Polymer Science , vol. 11 ( 2 ) : 251 – 287 .
   Google Scholar
• Matovich , M. and Pearson , J. 1969 . Spinning a Molten Threadline Steady-State Isothermal Viscous Flows . Industrial & Engineering Chemistry Fundamentals , vol. 8 ( 3 ) : 512 – 520 .
   Google Scholar
• Avenas , P. , Denn , M. and Petrie , C. 1975 . Mechanics of Steady Spinning of a Viscoelastic Liquid . American Institute of Chemical Engineers Journal , vol. 21 : 791
   Google Scholar
• Denn , M. and Marrucci , G. 1977 . Effect of a Relaxation Time Spectrum on the Mechanics of Polymer Melt Spinning . Journal of Non-Newtonian Fluid Mechanics , vol. 2 : 159 – 168 .
   Google Scholar
• Chang , J. and Denn , M. 1979 . An Experimental Study of Isothermal Spinning of a Newtonian and a Viscoelastic Liquid . Journal of Non-Newtonian Fluid Mechanics , vol. 5 : 369 – 385 .
   Google Scholar
• Dupret , F. and Marchal , J. 1986 . Loss of Evolution in the Flow of Viscoelastic Fluids . Journal of Non-Newtonian Fluid Mechanics , vol. 20 : 143 – 171 .
   Google Scholar
• Tsou , J. and Bogue , D. 1985 . The Effect of Die Flow on the Dynamics of Isothermal Melt Spinning . Journal of Non-Newtonian Fluid Mechanics , vol. 17 ( 3 ) : 331 – 347 .
   Google Scholar
• Minoshima , W. and White , J. 1986 . Instability Phenomena in Tubular Film, and Melt Spinning of Rheologically Characterized High Density, Low Density and Linear Low Density Polyethylenes . Journal of Non-Newtonian Fluid Mechanics , vol. 19 ( 3 ) : 275 – 302 .
   Google Scholar
• Keunings , R. , Crochet , M. and Denn , M. 1983 . Profile Development in Continuous Drawing of Viscoelastic Liquids . Industrial & Engineering Chemistry Fundamentals , vol. 22 ( 3 ) : 347 – 355 .
   Google Scholar
• Spearotand , J. and Metzner , A. 1972 . Isothermal Spinning of Molten Polyethylenes . Journal of Rheology , vol. 16 ( 3 ) : 495 – 518 .
   Google Scholar
• Ishihara , H. and Kase , S. 1975 . Studies on Melt Spinning. V. Draw Resonance As a Limit Cycle . Journal of Applied Polymer Science , vol. 19 ( 2 ) : 557 – 566 .
   Google Scholar
• Ishihara , H. and Kase , S. 1976 . Studies on Melt Spinning. VI. Simulation of Draw Resonance Using Newtonian and Power Law Viscosities . Journal of Applied Polymer Science , vol. 20 ( 1 ) : 169 – 191 .
   Google Scholar
• Weinberger , C. , Cruz-SaenzKase , G. and Donnelly , G. 1976 . Onset of Draw Resonance During Isothermal Melt Spinning: A Comparison Between Measurements and Predictions . American Institute of Chemical Engineers Journal , vol. 22 ( 3 ) : 441 – 448 .
   Google Scholar
• Fisher , R. , Denn , M. and Tanner , R. 1980 . Initial Profile Development in Melt Spinning . Industrial & Engineering Chemistry Fundamentals , vol. 19 ( 2 ) : 195 – 197 .
   Google Scholar
• Revenu , P. , Guillet , J. and Carrot , C. 1993 . Elongational Flow of Polyethylenes in Isothermal Melt Spinning . Journal of Rheology , vol. 37 ( 6 ) : 1041 – 1056 .
   Google Scholar
• Papanastasiou , T. , Macosko , C. , Scriven , L. and Chen , Z. 1987 . Fiber Spinning of Viscoelastic Liquid . American Institute of Chemical Engineers Journal , vol. 33 : 834 – 842 .
   Google Scholar
• Bell , W. and Edie , D. 1987 . Measured Orientation and Internal Stress Distributions in Melt-Spun Fibers . Journal of Applied Polymer Science , vol. 33 ( 4 ) : 1089 – 1102 .
   Google Scholar
• Bell , W. and Edie , D. 1987 . Calculated Internal Stress Distributions in Melt-Spun Fibers . Journal of Applied Polymer Science , vol. 33 ( 4 ) : 1073 – 1088 .
   Google Scholar
• Fulchiron , R. , Verney , V. , Michel , A. and Roustant , J. 1995 . Correlations Between Relaxation Time Spectrum and Melt Spinning Behavior of Polypropylene. II: Melt Spinning Simulation from Relaxation Time Spectrum . Polymer Engineering and Science , vol. 35 ( 6 ) : 513 – 518 .
   Google Scholar
• Fulchiron , R. , Verney , V. , Michel , A. and Roustant , J. 1995 . Correlations Between Relaxation Time Spectrum and Melt Spinning Behavior of Polypropylene. II: Melt Spinning Simulation from Relaxation Time Spectrum . Polymer Engineering and Science , vol. 35 ( 6 ) : 518 – 527 .
   Google Scholar
• Zieminski , K. and Spruiell , J. 1988 . On-Line Studies and Computer Simulation of the Melt Spinning of Nylon-66 Filaments . Journal of Applied Polymer Science , vol. 35 ( 8 ) : 2223 – 2245 .
   Google Scholar
• Sampers , J. and Leblans , P. 1988 . An Experimental and Theoretical Study of the Effect of the Elongational History on the Dynamics of Isothermal Melt Spinning . Journal of Non-Newtonian Fluid Mechanics , vol. 30 ( 2 ) : 325 – 342 .
   Google Scholar
• Giesekus , H. 1982 . A Simple Constitutive Equation for Polymer Fluids Based on the Concept of Deformation-Dependent Tensorial Mobility . Journal of Non-Newtonian Fluid Mechanics , vol. 11 ( 1–2 ) : 69 – 109 .
   Google Scholar
• Giesekus , H. 1982 . A Unified Approach to a Variety of Constitutive Models for Polymer Fluids Based on the Concept of Configuration-Dependent Molecular Mobility . Rheologica Acta , vol. 21 ( 4 ) : 366 – 375 .
   Google Scholar
• Yoo , J. and Choi , H. 1989 . On the Steady Simple Shear Flows of the One-Mode Giesekus Fluid . Rheologica Acta , vol. 28 ( 1 ) : 13 – 24 .
   Google Scholar
• Fisher , R. and Denn , M. 1977 . Mechanics of Nonisothermal Polymer Melt Spinning . American Institute of Chemical Engineers Journal , vol. 23 : 23 – 28 .
   Google Scholar
• Petrie , C. and Denn , M. 1976 . Instabilities in Polymer Processing . American Institute of Chemical Engineers Journal , vol. 22 ( 2 ) : 209 – 236 .
   Google Scholar
• Denn , M. 1980 . Continuous Drawing of Liquids to Form Fibers . Annual Review of Fluid Mechanics , vol. 12 ( 1 ) : 365 – 387 .
   Google Scholar
• Larson , R. 1992 . Instabilities in Viscoelastic Flows . Rheologica Acta , vol. 31 ( 3 ) : 213 – 263 .
   Google Scholar
• Beris , A. and Liu , B. 1988 . Time-Dependent Fiber Spinning Equations. I. Analysis of the Mathematical Behavior. II. Analysis of the Stability of Numerical Approximations . Journal of Non-Newtonian Fluid Mechanics , vol. 26 : 341 – 394 .
   Google Scholar
• Liu , B. and Beris , A. 1988 . Time-Dependent Fiber Spinning Equations. 2. Analysis of the Stability of Numerical Approximations . Journal of Non-Newtonian Fluid Mechanics , vol. 26 : 363
   Google Scholar
• Papanastasiou , T. , Malamataris , N. and Ellwood , K. 1992 . A New Outflow Boundary Condition . International Journal for Numerical Methods in Fluids , vol. 14 ( 5 ) : 587 – 608 .
   Google Scholar
• Papanastasiou , T. , Dimitriadis , L. , Scriven , L. , Macosko , C. and Sani , R. 1996 . On the Inlet Stress Condition and Admissibility of Solution of Fiber Spinning . Advances in Polymer Technology , vol. 15 : 237 – 244 .
   Google Scholar
• Bechtel , S. , Cao , J. and Forest , M. 1993 . Illustration of An Optimization Procedure for Fiber-Spinning Operating Conditions: Maximum Draw Ratio Under a Maxwell Thin-Filament Model . Journal of Rheology , vol. 37 ( 2 ) : 237 – 287 .
   Google Scholar
• Iyengar , V. and Co , A. Film Casting of a Modified Giesekus Fluid: A Steady-State Analysis . Journal of Non-Newtonian Fluid Mechanics , vol. 48 ( 1–2 )
   Google Scholar
• Iyengar , V. and Co , A. 1996 . Film Casting of a Modified Giesekus Fluid: Stability Analysis . Chem. Eng. Sci , vol. 51 : 1417
   Google Scholar
• Ramanan , V. , Bechtel , S. , Gauri , V. , Koelling , K. and Forest , M. 1997 . Exploiting Accurate Spinline Measurements for Elongational Material Characterization . Journal of Rheology , vol. 41 ( 2 ) : 283 – 306 .
   Google Scholar
• Gunter , S. , Townsend , P. and Webster , M. 1996 . The Simulation of Some Model Viscoelastic Extensional Flows . International Journal for Numerical Methods in Fluids , vol. 23 ( 7 ) : 691 – 710 .
   Google Scholar
• Yao , M. , McKinley , G. and Debbaut , B. 1998 . Extensional Deformation, Stress Relaxation and Necking Failure of Viscoelastic Filaments . Journal of Non-Newtonian Fluid Mechanics , vol. 79 ( 2 ) : 469 – 501 .
   Google Scholar
• Georgiou , G. and Vlassopoulos , D. 1998 . On the Stability of the Simple Shear Flow of a Johnson-Segalman Fluid . Journal of Non-Newtonian Fluid Mechanics , vol. 75 : 77 – 97 .
   Google Scholar
• Sureshkumar , R. , Smith , M. , Armstrong , R. and Brown , R. 1999 . Linear Stability and Dynamics of Viscoelastic Flows Using Time-Dependent Numerical Simulations . Journal of Non-Newtonian Fluid Mechanics , vol. 82 ( 57 ) : 104
   Google Scholar
• Bernardin , D. 1999 . Theoretical Study of Some Transient Couette Flows of Viscoelastic Fluids in Inertial Devices . Journal of Non-Newtonian Fluid Mechanics , vol. 88 ( 1 ) : 1 – 30 .
   Google Scholar
• Forest , M. , Wang , Q. and Bechtel , S. 1997 . 1-D Isothermal Spinning Models for Liquid Crystalline Polymer Fibers . Journal of Rheology , vol. 41 : 821 – 850 .
   Google Scholar
• Forest , M. , Zhou , H. and Wang , Q. 1999 . Model Study of the Spinning Thermoplastic Liquid Crystalline Polymers: Fiber Performance Predictions and Bounds on Throughput . Journal of Non-Newtonian Fluid Mechanics , vol. 82 ( 57 ) : 104
   Google Scholar
• Slattery , J. and Lee , S. 2000 . Analysis of Melt Spinning . Journal of Non-Newtonian Fluid Mechanics , vol. 89 ( 3 ) : 273 – 286 .
   Google Scholar
• Doufas , A. , McHugh , A. and Miller , C. Simulation of Melt Spinning Including Flow-Induced Crystallization. Part I. Model Development and Predictions . Journal of Non-Newtonian Fluid Mechanics , vol. 92 ( 1 )
   Google Scholar
• McKinley , G. , Brauner , O. and Yao , M. . Filament Stretching Rheometry and the Extensional Viscosity of Dilute and Concentrated Polymer Solutions . 1st International Symposium on Applied Rheology . pp. 65 – 71 .
   Google Scholar
• Lee , J. , Jung , H. , Kim , S. and Hyun , J. 2001 . Effect of Fluid Viscoelasticity on the Draw Resonance Dynamics of Melt Spinning . Journal of Non-Newtonian Fluid Mechanics , vol. 99 ( 2 ) : 159 – 166 .
   Google Scholar
• Joo , Y. , Sun , J. , Smith , M. , Armstrong , R. , Brown , R. and Ross , R. 2002 . Two-Dimensional Numerical Analysis of Non-Isothermal Melt Spinning With and Without Phase Transition . Journal of Non-Newtonian Fluid Mechanics , vol. 102 ( 1 ) : 37 – 70 .
   Google Scholar
• Gou , Z. and Mchugh , A. 2004 . Two-Dimensional Modeling of Dry Spinning of Polymer Fibers . Journal of Non-Newtonian Fluid Mechanics , vol. 118 ( 1 ) : 121 – 136 .
   Google Scholar
• Xue , S. , Tanner , R. and Phan-Thien , N. 2004 . Numerical Modeling of Transient Viscoelastic Flows . Journal of Non-Newtonian Fluid Mechanics , vol. 118 ( 1 ) : 121 – 136 .
   Google Scholar
• Surana , K. , Ahmadi , A. and Reddy , J. 2002 . The k-Version of Finite Element Method for Self-Adjoint Operators in BVP . International Journal of Computational Engineering Sciences , vol. 3 ( 2 ) : 155 – 218 .
   Google Scholar
• Surana , K. , Ahmadi , A. and Reddy , J. 2003 . The k-Version of Finite Element Method for Non-Self-Adjoint Operators in BVP . International Journal of Computational Engineering Sciences , vol. 4 ( 4 ) : 737 – 812 .
   Google Scholar
• Surana , K. , Ahmadi , A. and Reddy , J. 2004 . k-Version of Finite Element Method for Non-Linear Differential operators in BVP . International Journal of Computational Engineering Sciences , vol. 5 ( 1 ) : 133 – 207 .
   Google Scholar
• Surana , K. , Allu , S. and Reddy , J. 2007 . The k-Version of Finite Element Method for Initial Value Problems: Mathematical and Computational Framework . International Journal for Computational Methods in Engineering Science and Mechanics , vol. 8 ( 3 ) : 123 – 136 .
   Google Scholar
• Surana , K. , Anthoni , L. , Allu , S. and Reddy , J. 2008 . Strong and Weak Form of the Governing Differential Equations in Least Squares Finite Element Processes in h,p,k Framework . International Journal for Computational Methods in Engineering Science and Mechanics , vol. 9 ( 1 ) : 1 – 24 .
   Google Scholar
• Quinzani , L. , Armstrong , R. and Brown , R. 1995 . Use of Coupled Birefringence and LDV Studies of Flow Through a Planar Contraction to Test Constitutive Equations for Concentrated Polymer Solutions . Rheol. J. , vol. 39 ( 6 ) : 1201 – 1227 .
   Web of Science ®Google Scholar