메뉴 건너뛰기




Volumn 108, Issue 1-3, 2002, Pages 187-208

Stability analysis of polymer shear flows using the eXtended Pom-Pom constitutive equations

Author keywords

Planar viscoelastic shear flows; Pom Pom constitutive equations; Stability analysis

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; FINITE ELEMENT METHOD; ORDINARY DIFFERENTIAL EQUATIONS; POLYMERS;

EID: 0037203410     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0257(02)00130-1     Document Type: Article
Times cited : (77)

References (41)
  • 1
    • 0025492179 scopus 로고
    • A purely elastic instability in Taylor-Couette flow
    • R.G. Larson, E.S.G. Shaqfeh, S.J. Muller, A purely elastic instability in Taylor-Couette flow, J. Fluid Mech. 218 (1990) 573-600.
    • (1990) J. Fluid Mech. , vol.218 , pp. 573-600
    • Larson, R.G.1    Shaqfeh, E.S.G.2    Muller, S.J.3
  • 2
    • 0032051411 scopus 로고    scopus 로고
    • Effect of axial flow on viscoelastic Taylor-Couette instability
    • M.D. Graham, Effect of axial flow on viscoelastic Taylor-Couette instability, J. Fluid Mech. 360 (1998) 341-374.
    • (1998) J. Fluid Mech. , vol.360 , pp. 341-374
    • Graham, M.D.1
  • 3
    • 0030291976 scopus 로고    scopus 로고
    • Rheological and geometric scaling of purely elastic flow instabilities
    • G.H. McKinley, P. Pakdel, A. z̈tekin, Rheological and geometric scaling of purely elastic flow instabilities, J. Non-Newtonian Fluid Mech. 67 (1996) 19-47.
    • (1996) J. Non-Newtonian Fluid Mech. , vol.67 , pp. 19-47
    • McKinley, G.H.1    Pakdel, P.2    Öztekin, A.3
  • 4
    • 0344936448 scopus 로고    scopus 로고
    • Purely elastic instabilities in viscometric flows
    • E.S.G. Shaqfeh, Purely elastic instabilities in viscometric flows, Annu. Rev. Fluid Mech. 28 (1996) 129-185.
    • (1996) Annu. Rev. Fluid Mech. , vol.28 , pp. 129-185
    • Shaqfeh, E.S.G.1
  • 5
    • 0034977746 scopus 로고    scopus 로고
    • Extrusion instabilities and wall slip
    • M.M. Denn, Extrusion instabilities and wall slip, Annu. Rev. Fluid Mech. 33 (2001) 265-287.
    • (2001) Annu. Rev. Fluid Mech. , vol.33 , pp. 265-287
    • Denn, M.M.1
  • 6
    • 0030702818 scopus 로고    scopus 로고
    • Experimental studies of interfacial instabilities in multilayer pressure-driven flow
    • B. Khomami, M.M. Ranjbaran, Experimental studies of interfacial instabilities in multilayer pressure-driven flow, Rheol. Acta 36 (1997) 345-366.
    • (1997) Rheol. Acta , vol.36 , pp. 345-366
    • Khomami, B.1    Ranjbaran, M.M.2
  • 7
    • 33751371137 scopus 로고
    • Instabilities in viscoelastic flows
    • R.G. Larson, Instabilities in viscoelastic flows, Rheol. Acta 31 (1992) 313-363.
    • (1992) Rheol. Acta , vol.31 , pp. 313-363
    • Larson, R.G.1
  • 11
    • 0035398112 scopus 로고    scopus 로고
    • Differential constitutive equations for polymer melts: The eXtended Pom-Pom model
    • W.M.H. Verbeeten, G.W.M. Peters, F.P.T. Baaijens, Differential constitutive equations for polymer melts: The eXtended Pom-Pom model, J. Rheol. 45 (4) (2001) 823-844.
    • (2001) J. Rheol. , vol.45 , Issue.4 , pp. 823-844
    • Verbeeten, W.M.H.1    Peters, G.W.M.2    Baaijens, F.P.T.3
  • 13
    • 34250073348 scopus 로고
    • On the numerical stability of mixed finite-element methods for viscoelastic flows governed by differential constitutive equations
    • R.A. Brown, M.J. Szady, P.J. Northey, R.C. Armstrong, On the numerical stability of mixed finite-element methods for viscoelastic flows governed by differential constitutive equations, Theor. Comput. Fluid Dyn. 5 (1993) 77-106.
    • (1993) Theor. Comput. Fluid Dyn. , vol.5 , pp. 77-106
    • Brown, R.A.1    Szady, M.J.2    Northey, P.J.3    Armstrong, R.C.4
  • 14
    • 0012859558 scopus 로고    scopus 로고
    • Successes and failures of discontinuous galerkin methods in viscoelastic fluid analysis
    • B. Cockburn, G.E. Karniadakis, C.-W. Shu (Eds.), Number 11 in Lecture Notes in Computational Science and Engineering, Springer, Berlin
    • A.C.B. Bogaerds, W.M.H. Verbeeten, F.P.T. Baaijens, Successes and failures of discontinuous galerkin methods in viscoelastic fluid analysis, in: B. Cockburn, G.E. Karniadakis, C.-W. Shu (Eds.), Discontinuous Galerkin Methods, Number 11 in Lecture Notes in Computational Science and Engineering, Springer, Berlin, 2000, pp. 263-270.
    • (2000) Discontinuous Galerkin Methods , pp. 263-270
    • Bogaerds, A.C.B.1    Verbeeten, W.M.H.2    Baaijens, F.P.T.3
  • 16
    • 0000928050 scopus 로고
    • On the stability of three-dimensional disturbances of viscous flow between parallel walls
    • Ser. A
    • H.B. Squire, On the stability of three-dimensional disturbances of viscous flow between parallel walls, Proc. R. Soc. London, Ser. A 142 (621) (1933) 129-155.
    • (1933) Proc. R. Soc. London , vol.142 , Issue.621 , pp. 129-155
    • Squire, H.B.1
  • 17
    • 36849114667 scopus 로고
    • Stability of a relaxation-type viscoelastic fluid with slight elasticity
    • G. Tlapa, B. Bernstein, Stability of a relaxation-type viscoelastic fluid with slight elasticity, Phys. Fluids 13 (3) (1970) 565-568.
    • (1970) Phys. Fluids , vol.13 , Issue.3 , pp. 565-568
    • Tlapa, G.1    Bernstein, B.2
  • 18
    • 0000759154 scopus 로고    scopus 로고
    • Predicting low density polyethylene melt rheology in elongational and shear flows with 'Pom-Pom' constitutive equations
    • N.J. Inkson, T.C.B. McLeish, O.G. Harlen, D.J. Groves, Predicting low density polyethylene melt rheology in elongational and shear flows with 'Pom-Pom' constitutive equations, J. Rheol. 43 (4) (1999) 873-896.
    • (1999) J. Rheol. , vol.43 , Issue.4 , pp. 873-896
    • Inkson, N.J.1    McLeish, T.C.B.2    Harlen, O.G.3    Groves, D.J.4
  • 19
    • 0034817960 scopus 로고    scopus 로고
    • Using the Pom-Pom equations to analyze polymer melts in exponential shear
    • R.S. Graham, T.C.B. McLeish, O.G. Harlen, Using the Pom-Pom equations to analyze polymer melts in exponential shear, J. Rheol. 45 (1)(2001) 275-290.
    • (2001) J. Rheol. , vol.45 , Issue.1 , pp. 275-290
    • Graham, R.S.1    McLeish, T.C.B.2    Harlen, O.G.3
  • 20
    • 0031675952 scopus 로고    scopus 로고
    • Molecular constitutive equations for a class of branched polymers: The Pom-Pom polymer
    • T.C.B. McLeish, R.G. Larson, Molecular constitutive equations for a class of branched polymers: the Pom-Pom polymer, J. Rheol. 42 (1) (1998) 81-110.
    • (1998) J. Rheol. , vol.42 , Issue.1 , pp. 81-110
    • McLeish, T.C.B.1    Larson, R.G.2
  • 21
    • 0000077371 scopus 로고    scopus 로고
    • Molecular drag-strain coupling in branched polymer melts
    • R.J. Blackwell, T.C.B. McLeish, O.G. Harlen, Molecular drag-strain coupling in branched polymer melts, J. Rheol. 44 (1) (2000) 121-136.
    • (2000) J. Rheol. , vol.44 , Issue.1 , pp. 121-136
    • Blackwell, R.J.1    McLeish, T.C.B.2    Harlen, O.G.3
  • 22
    • 0022795184 scopus 로고
    • Linear stability of plane couette flow of an upper convected maxwell fluid
    • M. Renardy, Y. Renardy, Linear stability of plane couette flow of an upper convected maxwell fluid, J. Non-Newtonian Fluid Mech. 22 (1986) 23-33.
    • (1986) J. Non-Newtonian Fluid Mech. , vol.22 , pp. 23-33
    • Renardy, M.1    Renardy, Y.2
  • 23
    • 0033080138 scopus 로고    scopus 로고
    • An investigation of interfacial instabilities in the superposed channel flow of viscoelastic fluids
    • H.K. Ganpule, B. Khomami, An investigation of interfacial instabilities in the superposed channel flow of viscoelastic fluids, J. Non-Newtonian Fluid Mech. 81 (1999) 27-69.
    • (1999) J. Non-Newtonian Fluid Mech. , vol.81 , pp. 27-69
    • Ganpule, H.K.1    Khomami, B.2
  • 24
    • 0003600453 scopus 로고
    • Numerical analysis of spectral methods: Theory and applications
    • Society for Industrial and Applied Mathematics, Philadelphia
    • D. Gottlieb, S.A. Orszag, Numerical analysis of spectral methods: Theory and applications, in: Proceedings of the Regional Conference Series in Applied Mathematics; 26, Society for Industrial and Applied Mathematics, Philadelphia, 1977.
    • (1977) Proceedings of the Regional Conference Series in Applied Mathematics , vol.26
    • Gottlieb, D.1    Orszag, S.A.2
  • 26
    • 0001481692 scopus 로고
    • Removal of infinite eigenvalues in the generalized matrix eigenvalue problem
    • D.A. Goussis, A.J. Pearlstein, Removal of infinite eigenvalues in the generalized matrix eigenvalue problem, J. Comput. Phys. 84 (1989) 242-246.
    • (1989) J. Comput. Phys. , vol.84 , pp. 242-246
    • Goussis, D.A.1    Pearlstein, A.J.2
  • 27
    • 0029379966 scopus 로고
    • A new mixed finite element method for computing viscoelastic flows
    • R. Guńette, M. Fortin, A new mixed finite element method for computing viscoelastic flows, J. Non-Newtonian Fluid Mech. 60 (1995) 27-52.
    • (1995) J. Non-Newtonian Fluid Mech. , vol.60 , pp. 27-52
    • Guénette, R.1    Fortin, M.2
  • 28
    • 0019607241 scopus 로고
    • Streamline Upwind/Petrov Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
    • A.N. Brooks, T.J.R. Hughes, Streamline Upwind/Petrov Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Eng. 32 (1982) 199- 259.
    • (1982) Comput. Methods Appl. Mech. Eng. , vol.32 , pp. 199-259
    • Brooks, A.N.1    Hughes, T.J.R.2
  • 29
    • 0033567393 scopus 로고    scopus 로고
    • Galerkin/least-square finite element methods for steady viscoelastic flows
    • Y. Fan, R.I. Tanner, N. Phan-Thien, Galerkin/least-square finite element methods for steady viscoelastic flows, J. Non-Newtonian Fluid Mech. 84 (1999) 233-256.
    • (1999) J. Non-Newtonian Fluid Mech. , vol.84 , pp. 233-256
    • Fan, Y.1    Tanner, R.I.2    Phan-Thien, N.3
  • 30
    • 0026853119 scopus 로고
    • Analysis of simple constitutive equations for viscoelastic liquids
    • A.I. Leonov, Analysis of simple constitutive equations for viscoelastic liquids, J. Non-Newtonian Fluid Mech. 42 (1992) 323-350.
    • (1992) J. Non-Newtonian Fluid Mech. , vol.42 , pp. 323-350
    • Leonov, A.I.1
  • 31
    • 0000064075 scopus 로고
    • On a linear instability of a plane parallel couette flow of viscoelastic fluid
    • V.A. Gorodtsov, A.I. Leonov, On a linear instability of a plane parallel couette flow of viscoelastic fluid, J. Appl. Math. Mech. 31 (1967) 310-319.
    • (1967) J. Appl. Math. Mech. , vol.31 , pp. 310-319
    • Gorodtsov, V.A.1    Leonov, A.I.2
  • 32
    • 0032951205 scopus 로고    scopus 로고
    • Structure of the spectrum in zero reynolds number shear flow of the UCM and Oldroyd-B liquids
    • H.J. Wilson, M. Renardy, Y. Renardy, Structure of the spectrum in zero reynolds number shear flow of the UCM and Oldroyd-B liquids, J. Non-Newtonian Fluid Mech. 80 (1999) 251-268.
    • (1999) J. Non-Newtonian Fluid Mech. , vol.80 , pp. 251-268
    • Wilson, H.J.1    Renardy, M.2    Renardy, Y.3
  • 33
    • 0033117138 scopus 로고    scopus 로고
    • Linear stability and dynamics of viscoelastic flows using time-dependent numerical simulations
    • R. Sureshkumar, M.D. Smith, R.C. Armstrong, R.A. Brown, Linear stability and dynamics of viscoelastic flows using time-dependent numerical simulations, J. Non-Newtonian Fluid Mech. 82 (1999) 57-104.
    • (1999) J. Non-Newtonian Fluid Mech. , vol.82 , pp. 57-104
    • Sureshkumar, R.1    Smith, M.D.2    Armstrong, R.C.3    Brown, R.A.4
  • 34
    • 0035961186 scopus 로고    scopus 로고
    • Local linear stability characteristics of viscoelastic periodic channel flow
    • R. Sureshkumar, Local linear stability characteristics of viscoelastic periodic channel flow, J. Non-Newtonian Fluid Mech. 97 (2001) 125-148.
    • (2001) J. Non-Newtonian Fluid Mech. , vol.97 , pp. 125-148
    • Sureshkumar, R.1
  • 35
    • 0032122340 scopus 로고    scopus 로고
    • Inertial effect on the stability of cone-and-plate flow. Part 2: Non-axisymmetric modes
    • Y. Renardy, D.O. Olagunju, Inertial effect on the stability of cone-and-plate flow. Part 2: Non-axisymmetric modes, J. Non-Newtonian Fluid Mech. 78 (1998) 27-45.
    • (1998) J. Non-Newtonian Fluid Mech. , vol.78 , pp. 27-45
    • Renardy, Y.1    Olagunju, D.O.2
  • 36
    • 0026890783 scopus 로고
    • Numerical instability of time-dependent flows
    • R.A. Keiller, Numerical instability of time-dependent flows, J. Non-Newtonian Fluid Mech. 43 (1992) 229-246.
    • (1992) J. Non-Newtonian Fluid Mech. , vol.43 , pp. 229-246
    • Keiller, R.A.1
  • 37
    • 0034307617 scopus 로고    scopus 로고
    • Finite element analysis of stability of two-dimensional viscoelastic flows to three-dimensional perturbations
    • M.D. Smith, R.C. Armstrong, R.A. Brown, R. Sureshkumar, Finite element analysis of stability of two-dimensional viscoelastic flows to three-dimensional perturbations, J. Non-Newtonian Fluid Mech. 93 (2000) 203-244.
    • (2000) J. Non-Newtonian Fluid Mech. , vol.93 , pp. 203-244
    • Smith, M.D.1    Armstrong, R.C.2    Brown, R.A.3    Sureshkumar, R.4
  • 38
    • 0023451658 scopus 로고
    • Pseudo-spectral analysis of the stability of pressure-driven flow of a giesekus fluid between parallel planes
    • F.J. Lim, W.R. Schowalter, Pseudo-spectral analysis of the stability of pressure-driven flow of a giesekus fluid between parallel planes, J. Non-Newtonian Fluid Mech. 26 (1987) 135-142.
    • (1987) J. Non-Newtonian Fluid Mech. , vol.26 , pp. 135-142
    • Lim, F.J.1    Schowalter, W.R.2
  • 40
    • 0034332593 scopus 로고    scopus 로고
    • Location of the continuous spectrum in complex flows of the UCM fluid
    • M. Renardy, Location of the continuous spectrum in complex flows of the UCM fluid, J. Non-Newtonian Fluid Mech. 94 (2000) 75-85.
    • (2000) J. Non-Newtonian Fluid Mech. , vol.94 , pp. 75-85
    • Renardy, M.1
  • 41
    • 0034332858 scopus 로고    scopus 로고
    • Numerical observations on the continuous spectrum of the linearized viscoelastic operator in shear dominated complex flows
    • R. Sureshkumar, Numerical observations on the continuous spectrum of the linearized viscoelastic operator in shear dominated complex flows, J. Non-Newtonian Fluid Mech. 94 (2000) 205-211.
    • (2000) J. Non-Newtonian Fluid Mech. , vol.94 , pp. 205-211
    • Sureshkumar, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.