Skip to main content
Log in

On the multi-scale description of micro-structured fluids composed of aggregating rods

  • Original Article
  • Published:
Continuum Mechanics and Thermodynamics Aims and scope Submit manuscript

Abstract

When addressing the flow of concentrated suspensions composed of rods, dense clusters are observed. Thus, the adequate modelling and simulation of such a flow requires addressing the kinematics of these dense clusters and their impact on the flow in which they are immersed. In a former work, we addressed a first modelling framework of these clusters, assumed so dense that they were considered rigid and their kinematics (flow-induced rotation) were totally defined by a symmetric tensor \({\mathbf {c}}\) with unit trace representing the cluster conformation. Then, the rigid nature of the clusters was relaxed, assuming them deformable, and a model giving the evolution of both the cluster shape and its microstructural orientation descriptor (the so-called shape and orientation tensors) was proposed. This paper compares the predictions coming from those models with finer-scale discrete simulations inspired from molecular dynamics modelling.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Abisset-Chavanne, E., Mezher, R., Le Corre, S., Ammar, A., Chinesta, F.: Kinetic theory microstructure modeling in concentrated suspensions. Entropy 15, 2805–2832 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  2. Abisset-Chavanne, E., Ferec, J., Ausias, G., Cueto, E., Chinesta, F., Keunings, R.: A second-gradient theory of dilute suspensions of flexible rods in a Newtonian fluid. Arch. Comput. Methods Eng. 22, 511–527 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  3. Abisset-Chavanne, E., Chinesta, F., Ferec, J., Ausias, G., Keunings, R.: On the multiscale description of dilute suspensions of non-Brownian rigid clusters composed of rods. J. Non Newton. Fluid Mech. 222, 34–44 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  4. Advani, S., Tucker, C.: Closure approximations for three-dimensional structure tensors. J. Rheol. 34, 367–386 (1990)

    Article  ADS  Google Scholar 

  5. 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 Newt. Fluid Mech. 139, 153–176 (2006)

    Article  MATH  Google Scholar 

  6. 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 Newt. Fluid Mech. 144, 98–121 (2007)

    Article  MATH  Google Scholar 

  7. Batchelor, G.K.: The stress system in a suspension of force-free particles. J. Fluid Mech. 41, 545–570 (1970)

    Article  ADS  MATH  Google Scholar 

  8. Binetruy, C., Chinesta, F., Keunings, R.: Flows in Polymers, Reinforced Polymers and Composites. A Multi-scale Approach. Springer Briefs in Applied Sciences and Technology. Springer, Berlin (2015)

    Google Scholar 

  9. Bird, R.B., Curtiss, C.F., Armstrong, R.C., Hassager, O.: Dynamic of Polymeric Liquid, Volume 2: Kinetic Theory. Wiley, New York (1987)

    Google Scholar 

  10. Chaubal, C.V., Srinivasan, A., Egecioglu, O., Leal, L.G.: Smoothed particle hydrodynamics techniques for the solution of kinetic theory problems. J. Non Newton. Fluid Mech. 70, 125–154 (1997)

    Article  Google Scholar 

  11. Chauviere, C., Lozinski, A.: Simulation of dilute polymer solutions using a Fokker–Planck equation. Comput. Fluids 33, 687–696 (2004)

    Article  MATH  Google Scholar 

  12. Chiba, K., Ammar, A., Chinesta, F.: On the fiber orientation in steady recirculating flows involving short fibers suspensions. Rheol. Acta 44, 406–417 (2005)

    Article  Google Scholar 

  13. 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. 113, 97–125 (2003)

    Article  MATH  Google Scholar 

  14. 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. 166, 578–592 (2011)

    Article  MATH  Google Scholar 

  15. Chinesta, F.: From single-scale to two-scales kinetic theory descriptions of rods suspensions. Arch. Comput. Methods Eng. 20(1), 1–29 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  16. Chinesta, F., Keunings, R., Leygue, A.: The Proper Generalized Decomposition for Advanced Numerical Simulations. A Primer Springerbriefs. Springer, Berlin (2014)

    Book  MATH  Google Scholar 

  17. 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 49, 1141–1155 (2010)

    Article  Google Scholar 

  18. 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. 19(2), 227–259 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  19. dell’Isola, F., Giorgio, I., Pawlikowski, M., Rizzi, N.L.: Large deformations of planar extensible beams and pantographic lattices: heuristic homogenization, experimental and numerical examples of equilibrium. Proc. R. Soc. Lond. A 472(2185), 20150790 (2016)

    Article  ADS  Google Scholar 

  20. Doi, M., Edwards, S.F.: The Theory of Polymer Dynamics. Clarendon Press, Oxford (1987)

    Google Scholar 

  21. Dupret, F., Verleye, V.: Modelling the flow of fibre suspensions in narrow gaps. In: Siginer, D.A., De Kee, D., Chabra, R.P. (eds.) Advances in the Flow and Rheology of Non-Newtonian Fluids. Rheology Series, pp. 1347–1398. Elsevier, Amsterdam (1999)

    Chapter  Google Scholar 

  22. Eremeyev, V.A., Lebedev, L.P., Altenbach, H.: Foundations of Micropolar Mechanics. Springer, Berlin (2012)

    MATH  Google Scholar 

  23. Folgar, F., Tucker, C.: Orientation behavior of fibers in concentrated suspensions. J. Reinf. Plast. Comp. 3, 98–119 (1984)

    Article  Google Scholar 

  24. Hand, G.L.: A theory of anisotropic fluids. J. Fluid Mech. 13, 33–62 (1962)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. Hinch, J., Leal, G.: The effect of Brownian motion on the rheological properties of a suspension of non-spherical particles. J. Fluid Mech. 52, 683–712 (1972)

    Article  ADS  MATH  Google Scholar 

  26. Hinch, J., Leal, G.: Constitutive equations in suspension mechanics. Part I. J. Fluid Mech. 71, 481–495 (1975)

    Article  ADS  MATH  Google Scholar 

  27. Hinch, J., Leal, G.: Constitutive equations in suspension mechanics. Part II. J. Fluid Mech. 76, 187–208 (1976)

    Article  ADS  MATH  Google Scholar 

  28. Jeffery, G.B.: The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A102, 161–179 (1922)

    Article  ADS  MATH  Google Scholar 

  29. Keunings, R.: On the Peterlin approximation for finitely extensible dumbells. J. Non-Newton. Fluid Mech. 68, 85–100 (1997)

    Article  Google Scholar 

  30. Keunings, R.: Micro-macro methods for the multiscale simulation viscoelastic flow using molecular models of kinetic theory. In: Binding, D.M., Walters, K. (eds.) Rheology Reviews, pp. 67–83, British Society of Rheology, Aberystwyth, UK (2004). http://www.bsr.org.uk/rheology_review.asp

  31. Kroger, M., Ammar, A., Chinesta, F.: Consistent closure schemes for statistical models of anisotropic fluids. J. Nonnewton. Fluid Mech. 149, 40–55 (2008)

    Article  MATH  Google Scholar 

  32. Lozinski, A., Chauviere, C.: A fast solver for Fokker-Planck equation applied to viscoelastic flows calculations: 2D FENE model. J. Comput. Phys. 189, 607–625 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  33. Ma, A., Chinesta, F., Mackley, M., Ammar, A.: The rheological modelling of carbon nanotube (CNT) suspensions in steady shear flows. Int. J. Mater. Form. 2, 83–88 (2008)

    Article  Google Scholar 

  34. Ma, A., Chinesta, F., Ammar, A., Mackley, M.: Rheological modelling of carbon nanotube aggregate suspensions. J. Rheol. 52(6), 1311–1330 (2008)

    Article  ADS  Google Scholar 

  35. Ma, A., Chinesta, F., Mackley, M.: The rheology and modelling of chemically treated carbon nanotube suspensions. J. Rheol. 53(3), 547–573 (2009)

    Article  ADS  Google Scholar 

  36. 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. 17/2, 26494, 1–14 (2007)

  37. Öttinger, H.C., Laso, M.: Smart polymers in finite element calculation. In: International Congress on Rheology, Brussel (1992)

  38. Petrie, C.: The rheology of fibre suspensions. J. Non-Newton. Fluid Mech. 87, 369–402 (1999)

    Article  MATH  Google Scholar 

  39. Pietraszkiewicz, W., Eremeyev, V.A.: On natural strain measures of the non-linear micropolar continuum. Int. J. Solids Struct. 46(3–4), 774–787 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  40. 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. 16, 1–30 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  41. Wapperom, P., Keunings, R.: Numerical simulation of branched polymer melts in transient complex flows using pom-pom models. J. Non Newton. Fluid Mech. 97, 267–281 (2001)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Francisco Chinesta.

Additional information

Communicated by Francesco dell’Isola.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Perez, M., Scheuer, A., Abisset-Chavanne, E. et al. On the multi-scale description of micro-structured fluids composed of aggregating rods. Continuum Mech. Thermodyn. 31, 955–967 (2019). https://doi.org/10.1007/s00161-018-0659-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00161-018-0659-1

Keywords

Navigation