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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: [email protected]
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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
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Copyright
© 2016 Cambridge University Press 

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