Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
Multi-scale Modeling and Simulation of Polymer Flow Kapitel lesen Erstes Kapitel lesen

2015 | OriginalPaper | Buchkapitel

2. Complex Flows of Micro/Nano Structured Fluids: Reinforced Polymer Composites

verfasst von : Christophe Binetruy, Francisco Chinesta, Roland Keunings

Erschienen in: Flows in Polymers, Reinforced Polymers and Composites

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The motion of an ellipsoidal particle immersed in a Newtonian fluid was studied in the pioneering work of Jeffery in 1922. Suspensions of industrial interest usually involve particles with a variety of shapes. Moreover, suspensions composed of rods (a limit case of an ellipsoid) aggregate, leading to clusters with particular shapes that exhibit, when immersed in a flow, an almost rigid motion. In this chapter, we revisit the modeling and simulation of suspensions involving rods throughout the different scales of description (microscopic, mesoscopic and macroscopic) and the different concentration regimes (dilute, semi-dilute, semi-concentrated and concentrated), involving gradually richer physics.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel Multi-scale Modeling and Simulation of Polymer Flow
Nächstes Kapitel Flows of Simple Fluids in Complex Microstructures: Composite Processing of Structural Polymer Composites
Literatur
1.
G.B. Jeffery, The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A102, 161–179 (1922)CrossRef
2.
R. Keunings, in Micro-Macro Methods for the Multiscale Simulation of Viscoelastic Flow Using Molecular Models of Kinetic Theory. eds. by D.M. Binding, K. Walters. Rheology Reviews (British Society of Rheology, Durham, 2004), pp. 67–98
3.
R.B. Bird, C.F. Curtiss, R.C. Armstrong, O. Hassager, in Dynamic of Polymeric Liquid. Kinetic Theory, vol 2 (Wiley, New York, 1987)
4.
M. Doi, S.F. Edwards, The Theory of Polymer Dynamics (Clarendon Press, Oxford, 1987)
5.
A. Ammar, F. Chinesta, A particle strategy for solving the Fokker-Planck equation governing the fibre orientation distribution in steady recirculating flows involving short fibre suspensions. Lect. Notes Comput. Sci. Eng. 43, 1–16 (2005)CrossRefMathSciNet
6.
C.V. Chaubal, A. Srinivasan, O. Egecioglu, L.G. Leal, Smoothed particle hydrodynamics techniques for the solution of kinetic theory problems. J. Non-Newtonian Fluid Mech. 70, 125–154 (1997)CrossRef
7.
C. Chauviere, A. Lozinski, Simulation of dilute polymer solutions using a Fokker-Planck equation. Comput. Fluids. 33, 687–696 (2004)CrossRefMATH
8.
F. Chinesta, G. Chaidron, A. Poitou, On the solution of the Fokker-Planck equation in steady recirculating flows involving short fibre suspensions. J. Non-Newtonian Fluid Mech. 113, 97–125 (2003)CrossRefMATH
9.
C. Cruz, L. Illoul, F. Chinesta, G. Regnier, Effects of a bent structure on the linear viscoelastic response of carbon nanotube diluted suspensions. Rheol. Acta 49, 1141–1155 (2010)CrossRef
10.
C. Cruz, F. Chinesta, G. Regnier, Review on the Brownian dynamics simulation of bead-rod-spring models encountered in computational rheology. Arch. Comput. Methods Eng. 19(2), 227–259 (2012)CrossRefMathSciNet
11.
H.C. Öttinger, M. Laso, in Smart Polymers in Finite-Element calculations, eds. by P. Moldenaers, R. Keunings. Theoretical and Applied Rheology, Proceedings on XIth International Congress on Rheology, vol. 1 (Elsevier, Amsterdam, 1992), pp. 286–288
12.
P. Wapperom, R. Keunings, V. Legat, The backward-tracking Lagrangian particle method for transient viscoelastic flows. J. Non-Newtonian Fluid Mech. 91, 273–295 (2000)CrossRefMATH
13.
P. Wapperom, R. Keunings, Numerical simulation of branched polymer melts in transient complex flows using pom-pom models. J. Non-Newtonian Fluid Mech. 97, 267–281 (2001)CrossRefMATH
14.
A. Lozinski, C. Chauviere, A fast solver for Fokker-Planck equation applied to viscoelastic flows calculations: 2D FENE model. J. Comput. Phys. 189, 607–625 (2003)CrossRefMATHMathSciNet
15.
A. Ammar, B. Mokdad, F. Chinesta, R. Keunings, A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids. J. Non-Newtonian Fluid Mech. 139, 153–176 (2006)CrossRefMATH
16.
A. Ammar, B. Mokdad, F. Chinesta, R. Keunings, A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids. Part II: transient simulation using space-time separated representations. J. Non-Newtonian Fluid Mech. 144, 98–121 (2007)
17.
F. Chinesta, A. Ammar, A. Leygue, R. Keunings, An overview of the proper generalized decomposition with applications in computational rheology. J. Non-Newtonian Fluid Mech. 166, 578–592 (2011)CrossRefMATH
18.
F. Chinesta, R. Keunings, A. Leygue, The Proper Generalized Decomposition for Advanced Numerical Simulations (Springer, New York, 2014)CrossRefMATH
19.
B. Mokdad, E. Pruliere, A. Ammar, F. Chinesta, On the simulation of kinetic theory models of complex fluids using the Fokker-Planck approach. Appl. Rheol. 17(2), 1–14, 26494 (2007)
20.
K. Chiba, A. Ammar, F. Chinesta, On the fiber orientation in steady recirculating flows involving short fibers suspensions. Rheol. Acta 44, 406–417 (2005)CrossRef
21.
R. Keunings, On the Peterlin approximation for finitely extensible dumbbells. J. Non-Newtonian Fluid Mech. 68, 85–100 (1997)CrossRef
22.
F. Folgar, C. Tucker, Orientation behavior of fibers in concentrated suspensions. J. Reinf. Plast. Comp. 3, 98–119 (1984)
23.
24.
25.
J. Hinch, G. Leal, The effect of Brownian motion on the rheological properties of a suspension of non-spherical particles. J. Fluid Mech. 52, 683–712 (1972)CrossRefMATH
26.
J. Hinch, G. Leal, Constitutive equations in suspension mechanics. Part I. J. Fluid Mech. 71, 481–495 (1975)CrossRefMATH
27.
J. Hinch, G. Leal, Constitutive equations in suspension mechanics. Part II. J. Fluid Mech. 76, 187–208 (1976)CrossRefMATH
28.
S. Advani (ed.), Flow and Rheology in Polymer Composites Manufacturing (Elsevier, Amsterdam, 1994)
29.
J. Azaiez, K. Chiba, F. Chinesta, A. Poitou, State-of-the-art on numerical simulation of fiber-reinforced thermoplastic forming processes. Arch. Comput. Methods Eng. 9(2), 141–198 (2002)CrossRefMATH
30.
E. Cueto, R. Monge, F. Chinesta, A. Poitou, I. Alfaro, M. Mackley, Rheological modeling and forming process simulation of CNT nanocomposites. Int. J. Mater. Form. 3(2), 1327–1338 (2010)CrossRef
31.
M.A. Martinez, E. Cueto, M. Doblar, F. Chinesta, Natural element meshless simulation of injection processes involving short fiber suspensions. J. Non-Newtonian Fluid Mech. 115, 51–78 (2003)
32.
C. Tucker, Flow regimes for fiber suspensions in narrow gaps. J. Non-Newtonian Fluid Mech. 39, 239–268 (1991)
33.
A. Ma, F. Chinesta, M. Mackley, The rheology and modelling of chemically treated carbon nanotube suspensions. J. Rheol. 53(3), 547–573 (2009)CrossRef
34.
C. Petrie, The rheology of fibre suspensions. J. Non-Newtonian Fluid Mech. 87, 369–402 (1999)CrossRefMATH
35.
J. Ferec, G. Ausias, M.C. Heuzey, P. Carreau, Modeling fiber interactions in semiconcentrated fiber suspensions. J. Rheol. 53(1), 49–72 (2009)CrossRef
36.
J. Wang, C.A. Silva, J.C. Viana, F.W.J. van Hattum, A.M. Cunha, C. Tucker, Prediction of fiber orientation in a rotating compressing and expanding mold. Polym. Eng. Sci. 48(7), 1405–1413 (2008)
37.
J. Wang, J. O’Gara, C. Tucker, An objective model for slow orientation kinetics in concentrated fiber suspensions: theory and rheological evidence. J. Rheol. 52(5), 1179–1200 (2008)
38.
J. Phelps, C. Tucker, An anisotropic rotary diffusion model for fiber orientation in short and long fiber thermoplastics. J. Non-Newtonian Fluid Mech. 156(3), 165–176 (2009)
39.
A. Ma, F. Chinesta, A. Ammar, M. Mackley, Rheological modelling of carbon nanotube aggregate suspensions. J. Rheol. 52(6), 1311–1330 (2008)CrossRef
40.
G. Ausias, X.J. Fan, R. Tanner, Direct simulation for concentrated fibre suspensions in transient and steady state shear flows. J. Non-Newtonian Fluid Mech. 135, 46–57 (2006)CrossRefMATH
41.
S. Le Corre, D. Caillerie, L. Orgéas, D. Favier, Behavior of a net of fibers linked by viscous interactions: theory and mechanical properties. J. Mech. Phys. Solids 52(2), 395–421 (2004)CrossRefMATHMathSciNet
42.
S. Le Corre, P. Dumont, L. Orgéas, D. Favier, Rheology of highly concentrated planar fiber suspensions. J. Rheol. 49(5), 1029 (2005)
43.
F. Chinesta, From single-scale to two-scales kinetic theory descriptions of rods suspensions. Arch. Comput. Methods Eng. 20(1), 1–29 (2013)CrossRefMathSciNet
44.
E. Abisset-Chavanne, R. Mezher, S. Le Corre, A. Ammar, F. Chinesta, Kinetic theory microstructure modeling in concentrated suspensions. Entropy 15, 2805–2832 (2013)CrossRefMathSciNet
45.
E. Abisset-Chavanne, F. Chinesta, J. Ferec, G. Ausias, R. Keunings, On the multiscale description of dilute suspensions of non-Brownian rigid clusters composed of rods. J. Non-Newtonian Fluid Mech. (in press)
46.
S. Advani, C. Tucker, The use of tensors to describe and predict fiber orientation in short fiber composites. J. Rheol. 31, 751–784 (1987)
47.
S. Advani, C. Tucker, Closure approximations for three-dimensional structure tensors. J. Rheol. 34, 367–386 (1990)
48.
F. Dupret, V. Verleye, in Modelling the Flow of Fibre Suspensions in Narrow Gaps, eds. by D.A. Siginer, D. De Kee, R.P. Chabra. Advances in the Flow and Rheology of Non-Newtonian Fluids (Elsevier, Rheology Series, Amsterdam, 1999), pp. 1347–1398
49.
M. Kroger, A. Ammar, F. Chinesta, Consistent closure schemes for statistical models of anisotropic fluids. J. Non-Newtonian Fluid Mech. 149, 40–55 (2008)CrossRef
50.
E. Pruliere, A. Ammar, N. El Kissi, F. Chinesta, Recirculating flows involving short fiber suspensions: numerical difficulties and efficient advanced micro-macro solvers. Arch. Comput. Methods Eng. State Art Rev. 16, 1–30 (2009)CrossRefMATH
51.
P. Grassia, J. Hinch, L.C. Nitsche, Computer simulations of brownian motion of complex systems. J. Fluid Mech. 282, 373–403 (1995)CrossRefMATHMathSciNet
52.
P. Grassia, J. Hinch, Computer simulations of polymer chain relaxation via brownian motion. J. Fluid Mech. 308, 255–288 (1996)CrossRefMATH
53.
54.
P. Dumont, S. Le Corre, L. Orgeas, D. Favier, A numerical analysis of the evolution of bundle orientation in concentrated fibre-bundle suspensions. J. Non-Newtonian Fluid Mech. 160, 76–92 (2009)CrossRefMATH
55.
J. Ferec, E. Abisset-Chavanne, G. Ausias, F. Chinesta, The use of interaction tensors to describe and predict rod interactions in rod suspensions. Rheol. Acta 53(5–6), 445–456 (2014)CrossRef
56.
E. Pichelin, T. Coupez, Finite element solution of the 3D mold filling for viscous incompressible fluid. Comput. Methods Appl. Mech. Eng. 163, 359 (1998)CrossRefMATHMathSciNet
57.
D. Gonzalez, E. Cueto, F. Chinesta, M. Doblare, A natural element updated Lagrangian strategy for free-surface fluid dynamics. J. Comput. Phys. 223(1), 127–150 (2007)CrossRefMATHMathSciNet
58.
T. Belytschko, Y. Krongauz, D. Organ, M. Fleming, P. Krysl, Meshless methods: an overview and recent developments. Comput. Methods Appl. Mech. Eng. 139, 3–47 (1998)CrossRef
59.
F. Chinesta, S. Cescotto, E. Cueto, P. Lorong, Natural Element Method for the Simulation of Structures and Processes (ISTE Wiley, London, 2011)MATH
60.
61.
V. Belikov, V. Ivanov, V. Kontorovich, S. Korytnik, A. Semenov, The non-sibsonian interpolation: a new method of interpolation of the values of a function on an arbitrary set of points. Comput. Math. Math. Phys. 37(1), 9–15 (1997)
62.
E. Cueto, M. Doblare, L. Gracia, Imposing essential boundary conditions in the natural element method by means of density-scaled alpha-shapes. Int. J. Numer. Methods Eng. 49(4), 519–546 (2000)CrossRefMATHMathSciNet
63.
J. Yvonnet, D. Ryckelynck, P. Lorong, F. Chinesta, A new extension of the natural element method for non-convex and discontinuous problems: the constrained natural element method. Int. J. Numer. Methods Eng. 60(8), 1452–1474 (2004)CrossRefMathSciNet
64.
J.A. Garcia, Ll. Gascon, E. Cueto, I. Ordeig, F. Chinesta, Meshless methods with application to resin transfer molding simulation. Comput. Methods Appl. Mech. Eng. 198, 27002709 (2009)
65.
E. Cueto, M. Laso, F. Chinesta, Meshless stochastic simulation of maicro-macro kinetic theory models. Int. J. Multiscale Comput. Eng. 9(1), 1–16 (2011)CrossRef
66.
E. Cueto, A. Ma, F. Chinesta, M. Mackley, Numerical simulation of spin coating processes involving functionalised carbon nanotube suspensions. Int. J. Mater. Form. 1(2), 89–99 (2008)CrossRef
67.
J. Yvonnet, P. Villon, F. Chinesta, Natural element approximations involving bubbles for treating mechanical models in incompressible media. Int. J. Numer. Methods Eng. 66(7), 1125–1152 (2006)CrossRefMATHMathSciNet
68.
A. Ma, F. Chinesta, M. Mackley, A. Ammar, The rheological modelling of carbon nanotube (CNT) suspensions in steady shear flows. Int. J. Mat. Form. 2, 83–88 (2008)CrossRef
69.
F. Chinesta, A. Ammar, A. Falco, M. Laso, On the reduction of stochastic kinetic theory models of complex fluids. Model. Simul. Mater. Sci. Eng. 15, 639–652 (2007)CrossRef
70.
R. Shanker, J.W. Gillespie, S.I. Güçeri, On the effect of nonhomogeneous flow fields on the orientation distribution and rheology of fiber suspensions. Polym. Eng. Sci. 31, 161–171 (1991)CrossRef
71.
R. Shanker, The effect of non homogeneous flow fields and hydrodynamic interactions on the rheology of fiber suspensions, Ph.D. dissertation, University of Delaware, 1991
72.
E. Fried, M.E. Gurtin, Tractions, balances, and boundary conditions for non-simple materials with application to liquid flow at small length scales. Arch. Ration. Mech. Anal. 182, 513–554 (2006)CrossRefMATHMathSciNet
73.
T. Kim, J. Dolbow, E. Fried, A numerical method for a second-gradient theory of incompressible fluid flow. J. Comput. Phys. 223, 551–570 (2007)
74.
E. Abisset-Chavanne, J. Ferec, G. Ausias, E. Cueto, F. Chinesta, R. Keunings, A second-gradient theory of dilute suspensions of flexible rods in a Newtonian fluid. Arch. Comput. Methods Eng. (in press)
Metadaten
Titel
Complex Flows of Micro/Nano Structured Fluids: Reinforced Polymer Composites
verfasst von
Christophe Binetruy
Francisco Chinesta
Roland Keunings
Copyright-Jahr
2015
Buch
Flows in Polymers, Reinforced Polymers and Composites

Print ISBN: 978-3-319-16756-5

Electronic ISBN: 978-3-319-16757-2

Copyright-Jahr: 2015

DOI
https://doi.org/10.1007/978-3-319-16757-2_2

Premium Partner

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen. 

    Zur Marktübersicht
    Bildnachweise