Kinetic theory microstructure modeling in concentrated suspensions

Entropy

Volumn 15, Issue 7, 2013, Pages 2805-2832

  Abisset Chavanne, Emmanuelle ^a   Mezher, Rabih ^a   Corre, Steven Le ^b   Ammar, Amine ^c   Chinesta, Francisco ^a  

^a INSTITUT DE RECHERCHE EN GÉNIE CIVIL ET MÉCANIQUE GEM   (France)

^b Centre National de la Recherche Scientifique   (France)

^c ARTS ET MÉTIERS PARISTECH   (France)

Author keywords

Aggregates; Concentrated suspensions; Fokker Planck equation; Kinetic theory; Micromechanics; Proper generalized decomposition

Indexed keywords

EID: 84880939144     PISSN: None     EISSN: 10994300     Source Type: Journal    
DOI: 10.3390/e15072805     Document Type: Article

References (56)

1. Jeffery, G.B. The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. 1922, A102, 161-179.
2. Doi, M.; Edwards, S.F. The Theory of Polymer Dynamics; Clarendon Press: Oxford, UK, 1987.
3. Bird, R.B.; Crutiss, C.F.; Armstrong, R.C.; Hassager, O. Dynamic of Polymeric Liquid. In Kinetic Theory; John Wiley and Sons: Hoboken, NJ, USA, 1987; Volume 2.
4. Keunings, R. Micro-macro methods for the multiscale simulation viscoelastic flow using molecular models of kinetic theory. In Rheology Reviews; Binding, D.M., Walters, K., Eds.; British Society of Rheology: 2004; pp. 67-98.
5. Advani, S.; Tucker, C. The use of tensors to describe and predict fiber orientation in short fiber composites. J. Rheol. 1987, 31, 751-784.
6. Keunings, R. On the Peterlin approximation for finitely extensible dumbells. J. Non-Newton. Fluid Mech. 1997, 68, 85-100.
7. Chiba, K.; Ammar, A.; Chinesta, F. On the fiber orientation in steady recirculating flows involving short fibers suspensions. Rheol. Acta 2005, 44, 406-417.
8. Dumont, P.; Le Corre, S.; Orgeas, L.; Favier, D. A numerical analysis of the evolution of bundle orientation in concentrated fibre-bundle suspensions. J. Non-Newton. Fluid Mech. 2009, 160, 76-92.
9. Folgar, F.; Tucker, Ch. Orientation behavior of fibers in concentrated suspensions. J. Reinf. Plast. Comp. 1984, 3, 98-119.
10. Hand, G.L. A theory of anisotropic fluids. J. Fluid Mech. 1962, 13, 33-62.
11. Batchelor, G.K. The stress system in a suspension of force-free particles. J. Fluid Mech. 1970, 41, 545-570.
12. Hinch, J.; Leal, G. The effect of Brownian motion on the rheological properties of a suspension of non-spherical particles. J. Fluid Mech. 1972, 52, 683-712.
13. Hinch, J.; Leal, G. Constitutive equations in suspension mechanics. Part I. J. Fluid Mech. 1975, 71, 481-495.
14. Hinch, J.; Leal, G. Constitutive equations in suspension mechanics. Part II. J. Fluid Mech. 1976, 76, 187-208.
15. Tucker, Ch. Flow regimes for fiber suspensions in narrow gaps. J. Non-Newton. Fluid Mech. 1991, 39, 239-268.
16. Advani, S. Flow and Rheology in Polymer Composites Manufacturing; Elsevier: Amsterdam, The Netherlands, 1994.
17. Azaiez, J.; Chiba, K.; Chinesta, F. Poitou, A. State-of-the-art on numerical simulation of fiber-reinforced thermoplastic forming processes. Arch. Comput. Methods Eng. 2002, 9, 141-198.
18. Cueto, E.; Monge, R.; Chinesta, F.; Poitou, A.; Alfaro, I.; Mackley, M. Rheological modeling and forming process simulation of CNT nanocomposites. Int. J. Mater. Form. 2010, 3, 1327-1338.
19. Petrie, C. The rheology of fibre suspensions. J. Non-Newton. Fluid Mech. 1999, 87, 369-402.
20. Ma, A.; Chinesta, F.; Mackley, M. The rheology and modelling of chemically treated Carbon Nanotube suspensions. J. Rheol. 2009, 53, 547-573.
21. Ferec, J.; Ausias, G.; Heuzey, M.C.; Carreau, P. Modeling fiber interactions in semiconcentrated fiber suspensions. J. Rheol. 2009, 53, 49-72.
22. Wang, J.; Silva, C.A.; Viana, J.C.; van Hattum, F.W.J.; Cunha, A.M.; Tucker, Ch. Prediction of fiber orientation in a rotating compressing and expanding mold. Polym. Eng. Sci. 2008, 48, 1405-1413.
23. Wang, J.; OGara, J.; Tucker, C. An objective model for slow orientation kinetics in concentrated fiber suspensions: Theory and rheological evidence. J. Rheol. 2008, 52, 1179-1200.
24. Phelps, J.; Tucker, Ch. An anisotropic rotary diffusion model for fiber orientation in short and long fiber thermoplastics. J. Non-Newton. Fluid Mech. 2009, 156, 165-176.
25. Ma, A.; Chinesta, F.; Ammar, A.; Mackley, M. Rheological modelling of Carbon Nanotube aggregate suspensions. J. Rheol. 2008, 52, 1311-1330.
26. Le Corre, S.; Caillerie, D.; Orgéas, L.; Favier, D. Behavior of a net of fibers linked by viscous interactions: Theory and mechanical properties. J. Mech. Phys. Solids 2004, 52, 395-421.
27. Le Corre, S.; Dumont, P.; Orgéas, L.; Favier, D. Rheology of highly concentrated planar fiber suspensions. J. Rheol. 2005, 49, 1029-1058.
28. Chinesta, F. From single-scale to two-scales kinetic theory descriptions of rods suspensions. Arch. Comput. Methods Eng. 2013, 20, 1-29.
29. Abisset, E.; Mezher, R.; Chinesta, F. Two-scales kinetic theory model of short fibers aggregates. Key Eng. Mater. 2013, 554-557, 391-401.
30. Ma, A.; Chinesta, F.; Mackley, M.; Ammar, A. The rheological modelling of Carbon Nanotube (CNT) suspensions in steady shear flows. Int. J. Mater. Form. 2008, 2, 83-88.
31. Advani, S.; Tucker, Ch. Closure approximations for three-dimensional structure tensors. J. Rheol. 1990, 34, 367-386.
32. Dupret, F.; Verleye, V. Modelling the Flow of Fibre Suspensions in Narrow Gaps. In Advances in the Flow and Rheology of Non-Newton. Fluids, Rheology Series; Siginer, D.A., De Kee, D., Chabra, R.P., Eds.; Elsevier: Amsterdam, The Netherlands, 1999; pp. 1347-1398.
33. Kroger, M.; Ammar, A.; Chinesta, F. Consistent closure schemes for statistical models of anisotropic fluids. J. Non-Newton. Fluid Mech. 2008, 149, 40-55.
34. Pruliere, E.; Ammar, A.; El Kissi, N.; Chinesta, F. Recirculating flows involving short fiber suspensions: Numerical difficulties and efficient advanced micro-macro solvers. Arch. Comput. Methods Eng. State Art Rev. 2009, 16, 1-30.
35. Grassia, P.; Hinch, J.; Nitsche, L.C. Computer simulations of brownian motion of complex systems. J Fluid Mech. 1995, 282, 373-403.
36. Grassia, P.; Hinch, J. Computer simulations of polymer chain relaxation via brownian motion. J Fluid Mech. 1996, 308, 255-288.
37. Cruz, C.; Illoul, L.; Chinesta, F.; Regnier, G. Effects of a bent structure on the linear viscoelastic response of Carbon Nanotube diluted suspensions. Rheol. Acta 2010, 49, 1141-1155.
38. Cruz, C.; Chinesta, F.; Regnier, G. Review on the Brownian dynamics simulation of bead-rod-spring models encountered in computational rheology. Arch. Comput. Methods Eng. 2012, 19, 227-259.
39. Bellomo, N. Modeling Complex Living Systems; Birkhauser: Boston, MA, USA, 2008.
40. Ammar, A.; Mokdad, B.; Chinesta, F.; Keunings, R. A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids. J. Non-Newton. Fluid Mech. 2006, 139, 153-176.
41. Ammar, A.; Mokdad, B.; Chinesta, F.; Keunings, R. 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-Newton. Fluid Mech. 2007, 144, 98-121.
42. Mokdad, B.; Pruliere, E.; Ammar, A.; Chinesta, F. On the simulation of kinetic theory models of complex fluids using the Fokker-Planck approach. Appl. Rheol. 2007, 17, 26494, 1-14.
43. Leonenko, G.M.; Phillips, T.N. On the solution of the Fokker-Planck equation using a high-order reduced basis approximation. Comput. Methods Appl. Mech. Eng. 2009, 199, 158-168.
44. Ammar, A.; Normandin, M.; Daim, F.; Gonzalez, D.; Cueto, E.; Chinesta, F. Non-incremental strategies based on separated representations: Applications in computational rheology. Commun. Math. Sci. 2010, 8, 671-695.
45. Ammar, A.; Normandin, M.; Chinesta, F. Solving parametric complex fluids models in rheometric flows. J. Non-Newton. Fluid Mech. 2010, 165, 1588-1601.
46. Mokdad, B.; Ammar, A.; Normandin, M.; Chinesta, F.; Clermont, J.R. A fully deterministic micro-macro simulation of complex flows involving reversible network fluid models. Math. Comput. Simul. 2010, 80, 1936-1961.
47. Chinesta, F.; Ammar, A.; Cueto, E. Recent advances and new challenges in the use of the Proper Generalized Decomposition for solving multidimensional models. Arch. Comput. Methods Eng. 2010, 17, 327-350.
48. Chinesta, F.; Ammar, A.; Leygue, A.; Keunings, R. An overview of the Proper Generalized Decomposition with applications in computational rheology. J. Non-Newton. Fluid Mech. 2011, 166, 578-592.
49. Chinesta, F.; Ladeveze, P.; Cueto, E. A short review in model order reduction based on Proper Generalized Decomposition. Arch. Comput. Methods Eng. 2011, 18, 395-404.
50. Chinesta, F.; Leygue, A.; Bordeu, F.; Aguado, J.V.; Cueto, E.; Gonzalez, D.; Alfaro, I.; Ammar, A.; Huerta, A. Parametric PGD based computational vademecum for efficient design, optimization and control. Arch. Comput. Methods Eng. 2013, 20/1, 31-59.
51. Gonzalez, D.; Cueto, E.; Chinesta, F.; Diez, P.; Huerta, A. SUPG-based stabilization of Proper Generalized Decompositions for high-dimensional advection-diffusion equations. Int. J. Numer. Methods Eng. in press.
52. Chaubal, C.; Srinivasan, A.; Egecioglu, O.; Leal, G. Smoothed particle hydrodynamics techniques for the solution of kinetic theory problems. J. Non-Newton. Fluid Mech. 1997, 70, 125-154.
53. Chinesta, F.; Chaidron, G.; Poitou, A. On the solution of the Fokker-Planck equation in steady recirculating flows involving short fibre suspensions. J. Non-Newton. Fluid Mech. 2003, 113, 97-125.
54. Ammar, A.; Chinesta, F. A Particle Strategy for Solving the Fokker-Planck Equation Governing the Fibre Orientation Distribution in Steady Recirculating Flows Involving Short Fibre Suspensions. In Lectures Notes on Computational Science and Engineering; Springer: Berlin/Heidelberg, Germany, 2005; Volume 43, pp. 1-16.
55. Chinesta, F.; Ammar, A.; Falco, A.; Laso, M. On the reduction of stochastic kinetic theory models of complex fluids. Model. Simul. Mater. Sci. Eng. 2007, 15, 639-652.
56. Ottinger, H.C. Stochastic Processes in Polymeric Fluids; Springer: Berlin/Heidelberg, Germany, 1996.