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2007 | OriginalPaper | Buchkapitel

1. Experiment as a Boundary-Value Problem

verfasst von : Ronald Panton, Saeid Kheirandish, Ph.D, Manfred Wagner, Prof.

Erschienen in: Springer Handbook of Experimental Fluid Mechanics

Verlag: Springer Berlin Heidelberg

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Abstract

A fluid flow experiment is an attempt to isolate a part of the world and measure flow and thermodynamic properties. A fluid is defined as a material that deforms continuously if a shear stress is applied. An internal flow situation has walls bounding the flow, but an inflow and outflow position must be controlled. An external flow problem has a uniform flow far from the body of interest. In both situations the state of flow at the boundary is controlled. In the mathematical representation of the flow, the flow conditions on the boundary are specified. This is the nature of the governing physics. If the boundary conditions depend on time the flow situation in the entire region must be specified at the initial time.

In what follows the major physical laws are outlined. In most cases tensor calculus in symbolic form is employed. Scalars are lightface type, vectors are boldface type, and tensors are boldface capitals. However, in cases where confusion is possible with tensor multiplications, index notation is employed. Scalars are then without an index, vectors have one index and tensors have two or more indices.

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Nächstes Kapitel Nondimensional Representation of the Boundary-Value Problem

1.1.

S.I. Green: Fluid Vorticies (Kluwer Academic, Dordrecht 1995)

1.2.

D.D. Joseph: Fluid Dynamics of Viscoelastic Liquids (Springer, Berlin 1990)MATH

1.3.

R.G. Larson: Constitutive Equations for Polymer Melts and Solutions (Butterworths, London 1988)

1.4.

M. Doi, S.F. Edwards: The Theory of Polymer Dynamics (Oxford Univ. Press, Oxford 1986)

1.5.

M.H. Wagner: Challenges in Nonlinear Rheology of Linear and Long-Chain Branched Polymer Melts (Proc. XIVth Int. Congr. On Rheology, Korea 2004)

1.6.

T.C.B. McLeish, S.T. Milner: Entangled dynamics and melt flow behavior of branched polymers, Adv. Polym. Sci. 143, 195–256 (1999)CrossRef

1.7.

M.H. Wagner, P. Rubio, H. Bastian: The molecular stress function model for polydisperse and polymer melts with dissipative convective constraint release, J. Rheol. 45, 1387–1412 (2001)CrossRef

1.8.

H. Bastian: Non-linear viscoelasticity of linear and long-chain-branched polymer melts in shear and extensional flows , Ph. D. Thesis (Universität Stuttgart, Stuttgart 2000), http://elib.uni-stuttgart.de/opus/volltexte/2001/894

1.9.

M.H. Wagner, P. Ehrecke: Dynamics of polymer melts in reversing shear flows, J. Non-Newtonian Fluid Mech. 76, 183–197 (1998)CrossRefMATH

1.10.

A.S. Lodge: Constitutive equations from molecular theories for polymer solutions, Rheol. Acta. 7, 379–392 (1968)CrossRefMATH

1.11.

E. van Ruymbeke, R. Keunings, V. Stéphenne, A. Hagenaars, C. Bailly: Evaluation of reptation models for predicting the linear viscoelastic properties of linear entangled polymers, Macromolecules 35, 2689–2699 (2002)CrossRef

1.12.

A.L. Frischknecht, S.T. Milner, A. Pryke, R.N. Young, R. Hawkins, T.C.B. McLeish: Rheology of three-arm asymmetric star polymer melts, Macromolecules 35, 4801–4820 (2002)CrossRef

1.13.

M.H. Wagner, J. Meissner: Network disentanglement and time-dependent flow behavior of polymer melts, Macromol. Chem. 181, 1533–1550 (1980)CrossRef

1.14.

C.W. Macosko: Rheology, Principles, Measurements and Applications (VCH, New York 1994)

1.15.

H.M. Laun: Description of the non-linear shear behavior of a low density polyethylene melt by means of an experimentally determined strain dependent memory function, Rheol. Acta. 17, 1–15 (1978)CrossRef

1.16.

M.H. Wagner: Analysis of time-dependent non-linear stress-growth data for shear and elongational flow of a low-density branched polyethylene melt, Rheol. Acta. 15, 136–142 (1976)CrossRef

1.17.

M.H. Wagner: Prediction of primary normal stress difference from shear viscosity data using a single integral constitutive equation, Rheol. Acta. 16, 43–50 (1977)CrossRef

1.18.

M.H. Wagner, S.E. Stephenson: The spike strain test for polymeric liquid and its relevance for irreversible destruction of network connectivity by deformation, Rheol. Acta. 18, 463–468 (1979)CrossRef

1.19.

M.H. Wagner, S.E. Stephenson: The irreversibility assumption of network disentanglement in flowing polymer melts and its effects on elastic recoil predictions, J. Rheol. 23, 489–504 (1979)CrossRef

1.20.

K. Osaki, S. Kimura, M. Kurata: Relaxation of shear and normal stresses in double-step shear deformations for a polystyrene solution. A test of Doi-Edwards theory for polymer rheology, J. Rheol. 25, 549–562 (1981)CrossRef

1.21.

M.H. Wagner: A constitutive analysis of uniaxial elongational flow data of a low-density polyethylene melt, J. Non-Newtonian Fluid Mech. 4, 39–55 (1978)CrossRef

1.22.

A.C. Papanastasiou, L.E. Scriven, C.W. Macosko: An integral constitutive equation for mixed flows: viscoelastic characterization, J. Rheol. 27, 387–410 (1983)CrossRef

1.23.

T. Samurkas, R.G. Larson, J.M. Dealy: Strong extensional and shearing flows of a branched polyethylene, J. Rheol. 33, 559–578 (1989)CrossRef

1.24.

P.K. Currie: Constitutive equations for polymer melts predicted by the Doi–Edwards and Curtiss-Bird kinetic theory models, J. Non-Newtonian Fluid Mech. 11, 53–68 (1982)CrossRefMATH

1.25.

M.H. Wagner, A. Demarmels: A constitutive analysis of extensional flows of polyisobutylene, J. Rheol. 34, 943–958 (1990)CrossRef

1.26.

O. Urakawa, M. Takahashi, T. Masuda, N.G. Ebrahimi: Damping functions and chain relaxation in uniaxial and biaxial elongation: comparison with the Doi-Edwards theory, Macromolecules 28, 7196–7201 (1995)CrossRef

1.27.

B.J.R. Scholtens, P.J.R. Leblans: Nonlinear viscoelasticity of noncrystalline EPDM rubber networks, J. Rheol. 30, 313–335 (1986)CrossRef

1.28.

M.H. Wagner: The nonlinear strain measure of polyisobutylene melt in general biaxial flow and its comparison to the Doi-Edwards model, Rheol. Acta. 29, 594–603 (1990)CrossRef

1.29.

D.S. Pearson, A. Kiss, L. Fetters, M. Doi: Flow-induced birefringence of concentrated polyisoprene solutions, J. Rheol. 33, 517–535 (1989)CrossRef

1.30.

G. Ianniruberto, G. Marrucci: A simple constitutive equation for entangled polymers with chain stretch, J. Rheol. 45, 1305–1318 (2001)CrossRef

1.31.

J. Fang, M. Kröger, H.M. Öttinger: A thermodynamically admissible reptation model for fast flows of entangled polymers: II. Model predictions for shear and extensional flows, J. Rheol. 44, 1293–1316 (2000)CrossRef

1.32.

T.C.B. McLeish, R.G. Larson: Molecular constitutive equations for a class of branched polymers: the pom-pom polymer, J. Rheol. 42, 81–110 (1998)CrossRef

1.33.

T.C.B. McLeish: Molecular rheology of H-polymers, Macromolecules 21, 1062–1070 (1988)CrossRef

1.34.

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, 873–896 (1999)CrossRef

1.35.

R.J. Blackwell, T.C.B. McLeish, O.G. Harlen: Molecular drag-strain coupling in branched polymer melts, J. Rheol. 44, 121–136 (2000)CrossRef

1.36.

R.G. Owens, T.N. Phillips: Computational Rheology (Imperial College Press, London 2002)CrossRefMATH

1.37.

P. Rubio, M.H. Wagner: Letter to the Editor: A note added to "Molecular constitutive equations for a class of branched polymers: The pom-pom model", J. Rheol. 43, 1709–1710 (1999)CrossRef

1.38.

P. Rubio, M.H. Wagner: LDPE melt rheology and the pom-pom polymer, J. Non-Newtonian Fluid Mech. 92, 245–259 (2000)CrossRefMATH

1.39.

R.J. Blackwell, O.G. Harlen, T.C.B. McLeish: Theoretical linear and non-linear rheology of symmetric treelike polymer melts, Macromolecules 34, 2579–2596 (2001)CrossRef

1.40.

P.J. Doerpinghaus, D.G. Baird: Accessing the branching architecture of sparsely branched metallocene-catalyzed polyethylenes using the pompom constitutive model, Macromolecules 35, 10087–10095 (2002)CrossRef

1.41.

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, 823–843 (2001)CrossRef

1.42.

N. Clemeur, R.P.G. Rutgers, B. Debbaut: On the evaluation of some differential formulations for the pom-pom constitutive model, Rheol. Acta. 42, 217–231 (2003)

1.43.

G. Marrucci, B. de Cindio: The stress relaxation of molten PMMA at large deformations and its theoretical interpretation, Rheol. Acta. 19, 68–75 (1980)CrossRef

1.44.

M.H. Wagner, J. Schaeffer: Constitutive equations from Gaussian slip-link network theories in polymer melt rheology, Rheol. Acta. 31, 22–31 (1992)CrossRef

1.45.

M.H. Wagner, J. Schaeffer: Rubbers and Polymer melts: Universal aspects of non-linear stress-strain relations, J. Rheol. 37, 643–661 (1993)CrossRef

1.46.

M.H. Wagner: The non-linear strain measure of polymer melts and rubbers: A unifying approach, Makromol. Chem. Macromol. Symp. 68, 95–108 (1993)CrossRef

1.47.

M.H. Wagner, J. Schaeffer: Assessment of non-linear strain measures for extensional and shearing flows of polymer melts, Rheol. Acta. 33, 506–516 (1994)CrossRef

1.48.

M.H. Wagner, J. Schaeffer: Nonlinear strain measures for general biaxial extension of polymer melts, Rheol. Acta. 36, 1–26 (1992)

1.49.

M.H. Wagner, M. Yamaguchi, M. Takahashi: Quantitative assessment of strain hardening of LDPE melts by MSF model, J. Rheol. 47, 779–793 (2003)CrossRef

1.50.

M.H. Wagner, J. Hepperle, H. Münstedt: Relating molecular structure of model branched polystyrene melts to strain-hardening by molecular stress function theory, J. Rheol. 48, 489–503 (2004)CrossRef

1.51.

M.H. Wagner, S. Kheirandish, M. Yamaguchi: Quantitative analysis of melt elongational behavior of LDPE/LLDPE blends, Rheol. Acta 44, 198–218 (2005)CrossRef

1.52.

M.H. Wagner, S. Kheirandish, K. Koyama, A. Nishioka, A. Minegishi, T. Takahashi: Modeling strain hardening of polydisperse polystyrene melts by molecular stress function theory 44, 235–243 (2005)

1.53.

P.G. de Gennes: Reptation of polymer chain in the presence of fixed obstacles, J. Chem. Phys. 55, 572–579 (1971)CrossRef

1.54.

G. Marrucci, N. Grizzutti: The free energy function of the Doi-Edwards theory: Analysis of instabilities in stress relaxation, J. Rheol. 27, 433–450 (1983)CrossRef

1.55.

G. Marrucci, J.J. Hermans: Non-linear viscoelasticity of concentrated polymeric liquids, Macromolecules 13, 380–387 (1980)CrossRef

1.56.

J. Hepperle: Einfluss der molekularen Struktur auf rheologische Eigenschaften von Polystyrol- und Polycarbonatschmelzen (Shaker, Aachen 2003)

Titel: Experiment as a Boundary-Value Problem
verfasst von: Ronald Panton
Saeid Kheirandish, Ph.D
Manfred Wagner, Prof.
Verlag: Springer Berlin Heidelberg
Buch: Springer Handbook of Experimental Fluid Mechanics
Print ISBN: 978-3-540-25141-5

Electronic ISBN: 978-3-540-30299-5

Copyright-Jahr: 2007
DOI: https://doi.org/10.1007/978-3-540-30299-5_1

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