Hostname: page-component-8448b6f56d-sxzjt Total loading time: 0 Render date: 2024-04-24T14:45:54.944Z Has data issue: false hasContentIssue false
  • English
  • Français

The effect of shear-thinning behaviour on rod orientation in filled fluids

Published online by Cambridge University Press:  01 June 2016

Julien Férec Open the ORCID record for Julien Férec [Opens in a new window] ,
Erwan Bertevas ,
Boo Cheong Khoo ,
Gilles Ausias  and
Nhan Phan-Thien
Julien Férec*
Affiliation:
Institut de Recherche Dupuy de Lôme (IRDL), Univ. Bretagne Sud, FRE CNRS 3744, IRDL, F-56100 Lorient, France
Erwan Bertevas
Affiliation:
Department of Mechanical Engineering, National University of Singapore, Singapore 119260, Singapore
Boo Cheong Khoo
Affiliation:
Department of Mechanical Engineering, National University of Singapore, Singapore 119260, Singapore
Gilles Ausias
Affiliation:
Institut de Recherche Dupuy de Lôme (IRDL), Univ. Bretagne Sud, FRE CNRS 3744, IRDL, F-56100 Lorient, France
Nhan Phan-Thien
Affiliation:
Department of Mechanical Engineering, National University of Singapore, Singapore 119260, Singapore
*
†Email address for correspondence: julien.ferec@univ-ubs.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

In the present article, the cell model (or self-consistent scheme) is used to derive constitutive equations for rod suspensions in non-Newtonian viscous matrices such as power-law, Ellis and Carreau fluids. It is found that the shear-thinning character of the matrix influences considerably the rod contribution to the stress tensor, but has no impact on the rod orientation dynamics: the same microstructure evolution as the one encountered in Newtonian fluids is obtained. The rod suspension behaves differently than the unfilled matrix in the sense that, depending on rod orientation, the onset of shear thinning in the composite occurs at lower or higher shear rates. Our analysis also provides a semi-analytical model for rod suspensions in an Ellis fluid, which appears to be suitable for predicting a Newtonian plateau at low shear rates and a shear-thinning behaviour at high shear rates. In addition, the model predictions are in good agreement with the shear viscosity measurements of glass-fibre-filled polystyrene melts (Chan et al., J. Rheol., vol. 22 (5), 1978, pp. 507–524), demonstrating its ability to describe the rheological behaviour of such polymer composites. Finally, the proposed approach is extended to a Carreau fluid although its solution requires the numerical solution of a set of partial differential equations.

JFM classification

Non-Newtonian Flows: Rheology Low-Reynolds-number flows: Slender-body theory Complex Fluids: Suspensions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 798 , 10 July 2016 , pp. 350 - 370
Check for updates
Copyright
© 2016 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Advani, S. G. & Tucker, C. L. 1987 The use of tensors to describe and predict fiber orientation in short fiber composites. J. Rheol. 31 (8), 751–784.Google Scholar
Advani, S. G. & Tucker, C. L. 1990 Closure approximations for three-dimensional structure tensors. J. Rheol. 34 (3), 367–386.CrossRefGoogle Scholar
Ait-Kadi, A. & Grmela, M. 1994 Modelling the rheological behaviour of fibre suspensions in viscoelastic media. J. Non-Newtonian Fluid Mech. 53, 65–81.Google Scholar
Azaiez, J. 1996 Constitutive equations for fiber suspensions in viscoelastic media. J. Non-Newtonian Fluid Mech. 66 (1), 35–54.CrossRefGoogle Scholar
Batchelor, G. K. 1971 The stress generated in a non-dilute suspension of elongated particles by pure straining motion. J. Fluid Mech. 46 (4), 813–829.Google Scholar
Bay, R. S.1991 Fiber orientation in injection-molded composites: a comparison of theory and experiment. PhD dissertation.Google Scholar
Beaulne, M. & Mitsoulis, E. 2003 Rheological characterization of fiber-filled polymer composites via constitutive modeling. J. Reinforced Plastics Compos. 22 (17), 1625–1640.Google Scholar
Becraft, M. L. & Metzner, A. B. 1992 The rheology, fiber orientation, and processing behavior of fiber filled fluids. J. Rheol. 36 (1), 143–174.CrossRefGoogle Scholar
Bird, R. B., Armstrong, R. C. & Hassager, O. 1987a Dynamics of Polymeric Liquids. Fluid Mechanics, 2nd edn. vol. 1. Wiley.Google Scholar
Bird, R. B., Curtiss, C. F., Armstrong, R. C. & Hassager, O. 1987b Dynamics of Polymeric Liquids. Kinetic Theory, 2nd edn. vol. 2. Wiley.Google Scholar
Chan, Y., White, J. L. & Oyanagi, Y. 1978 A fundamental study of the rheological properties of glass-fiber-reinforced polyethylene and polystyrene melts. J. Rheol. 22 (5), 507–524.Google Scholar
Chung, S. T. & Kwon, T. H. 1996 Coupled analysis of injection molding filling and fiber orientation, including in-plane velocity gradient effect. Polym. Compos. 17 (6), 859–872.Google Scholar
Cintra, J. S. & Tucker, C. L. 1995 Orthotropic closure approximations for flow-induced fiber orientation. J. Rheol. 39 (6), 1095–1122.Google Scholar
Czarnecki, L. & White, J. L. 1980 Shear flow rheological properties, fiber damage, and mastication characteristics of aramid-, glass-, and cellulose-fiber-reinforced polystyrene melts. J. Appl. Polym. Sci. 25 (6), 1217–1244.Google Scholar
Dinh, S. M. & Armstrong, R. C. 1984 A rheological equation of state for semiconcentrated fiber suspensions. J. Rheol. 28 (3), 207–227.Google Scholar
Doi, M. & Edwards, S. F. 1986 The Theory of Polymer Dynamics. Oxford Science Publications.Google Scholar
Dupret, F. & Verleye, V. 1999 Modeling the Flow of Fiber Suspensions in Narrow Gaps, 8th edn. vol. 2, pp. 19–29. Elsevier.Google Scholar
Férec, J. & Ausias, G. 2015 Rheological Modeling of Non-dilute Rod Suspensions, pp. 77–118. Wiley.Google Scholar
Férec, J., Heniche, M., Heuzey, M. C., Ausias, G. & Carreau, P. J. 2008 Numerical solution of the Fokker–Planck equation for fiber suspensions: application to the Folgar–Tucker–Lipscomb model. J. Non-Newtonian Fluid Mech. 155 (12), 20–29.Google Scholar
Férec, J., Heuzey, M.-C., Pérez-González, J., Vargas, L., Ausias, G. & Carreau, P. J. 2009 Investigation of the rheological properties of short glass fiber-filled polypropylene in extensional flow. Rheol. Acta 48 (1), 59–72.Google Scholar
Folgar, F. & Tucker, C. L. 1984 Orientation behavior of fibers in concentrated suspensions. J. Reinforced Plastics Compos. 3 (2), 98–119.Google Scholar
Gibson, A. G. & Toll, S. 1999 Mechanics of the squeeze flow of planar fibre suspensions. J. Non-Newtonian Fluid Mech. 82, 1–24.Google Scholar
Giesekus, H. 1962 Elasto-viskose flssigkeiten, fr die in stationren schichtstrmungen smtliche normalspannungskomponenten verschieden gross sind. Rheol. Acta 2 (01), 50–62.Google Scholar
Goddard, J. D. 1976a The stress field of slender particles oriented by a non-Newtonian extensional flow. J. Fluid Mech. 78 (1), 177–206.Google Scholar
Goddard, J. D. 1976b Tensile stress contribution of flow-oriented slender particles in non-Newtonian fluids. J. Non-Newtonian Fluid Mech. 1 (1), 1–17.Google Scholar
Goddard, J. D. 1978 Tensile behavior of powerlaw fluids containing oriented slender fibers. J. Rheol. 22 (6), 615–622.Google Scholar
Greene, J. P. & Wilkes, J. O. 1995 Steady-state and dynamic properties of concentrated fiber-filled thermoplastics. Polym. Engng Sci. 35 (21), 1670–1681.Google Scholar
Hinch, E. J. & Leal, L. G. 1975 Constitutive equations in suspension mechanics. Part 1. General formulation. J. Fluid Mech. 71 (3), 481–495.Google Scholar
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. 102, 161–179.Google Scholar
Kagarise, C., Miyazono, K., Mahboob, M., Koelling, K. W. & Bechtel, S. E. 2011 A constitutive model for characterization of shear and extensional rheology and flow induced orientation of carbon nanofiber/polystyrene melt composites. J. Rheol. 55 (4), 781–807.CrossRefGoogle Scholar
Kagarise, C., Xu, J., Wang, Y., Mahboob, M., Koelling, K. W. & Bechtel, S. E. 2010 Transient shear rheology of carbon nanofiber/polystyrene melt composites. J. Non-Newtonian Fluid Mech. 165 (34), 98–109.Google Scholar
Kitano, T. & Kataoka, T. 1980 The effect of the mixing methods on viscous properties of polyethylene melts filled with fibers. Rheol. Acta 19 (6), 753–763.Google Scholar
Kitano, T., Kataoka, T. & Nagatsuka, Y. 1984 Shear flow rheological properties of vinylon- and glass-fiber reinforced polyethylene melts. Rheol. Acta 23 (1), 20–30.Google Scholar
Mobuchon, C., Carreau, P. J., Heuzey, M.-C., Sepehr, M. & Ausias, G. 2005 Shear and extensional properties of short glass fiber reinforced polypropylene. Polym. Compos. 26 (3), 247–264.Google Scholar
Nishitani, Y., Sekiguchi, I., Hausnerova, B., Zdrazilova, N. & Kitano, T. 2007 Rheological properties of aminosilane surface treated short glass fibre reinforced polypropylenes. Part 1: steady shear and oscillatory flow properties in molten state. Polymer Polym. Compos. 15 (2), 111–119.Google Scholar
Ouari, N., Kaci, A., Tahakourt, A. & Chaouche, M. 2011 Rheological behaviour of fibre suspensions in non-Newtonian fluids. Appl. Rheol. 21 (5), 54801.Google Scholar
Phan-Thien, N., Fan, X. J., Tanner, R. I. & Zheng, R. 2002 Folgar–Tucker constant for a fibre suspension in a Newtonian fluid. J. Non-Newtonian Fluid Mech. 103 (2–3), 251–260.Google Scholar
Poslinski, A. J., Ryan, M. E., Gupta, R. K., Seshadri, S. G. & Frechette, F. J. 1988 Rheological behavior of filled polymeric systems I. Yield stress and shearthinning effects. J. Rheol. 32 (7), 703–735.Google Scholar
Rajabian, M., Dubois, C. & Grmela, M. 2005 Suspensions of semiflexible fibers in polymeric fluids: rheology and thermodynamics. Rheol. Acta 44 (5), 521–535.CrossRefGoogle Scholar
Ramazani, S. A., Ait-Kadi, A. & Grmela, M. 1997 Rheological modelling of short fiber thermoplastic composites. J. Non-Newtonian Fluid Mech. 73 (3), 241–260.Google Scholar
Ramazani, S. A., Ait-Kadi, A. & Grmela, M. 2001 Rheology of fiber suspensions in viscoelastic media: experiments and model predictions. J. Rheol. 45 (4), 945–962.Google Scholar
Sepehr, M., Carreau, P. J., Grmela, M., Ausias, G. & Lafleur, P. G. 2004 Comparison of rheological properties of fiber suspensions with model predictions. J. Polym. Engng 24 (6), 579–610.Google Scholar
Souloumiac, B. & Vincent, M. 1998 Steady shear viscosity of short fibre suspensions in thermoplastics. Rheol. Acta 37 (3), 289–298.Google Scholar
Wang, M. L. & Cheau, T. C. 1991 A constitutive approach for studying concentrated suspensions of rigid fibers in a non-Newtonian Ellis fluid. J. Chin. Inst. Engng 14 (5), 483–493.Google Scholar
White, J. L. & Czarnecki, L. 1980 Notes: on papers by Chan, White, and Oyanagi and by Goddard on elongational flow behavior of fiber-reinforced polymer melts. J. Rheol. 24 (4), 501–506.Google Scholar