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Suspensions in a tilted trough: second normal stress difference

Published online by Cambridge University Press:  21 September 2011

Étienne Couturier ,
François Boyer ,
Olivier Pouliquen  and
Élisabeth Guazzelli
Étienne Couturier
Affiliation:
IUSTI-CNRS UMR 6595, Polytech-Marseille, Aix-Marseille Université (U1), Technopôle de Château-Gombert, 13453 Marseille CEDEX 13, France
François Boyer*
Affiliation:
IUSTI-CNRS UMR 6595, Polytech-Marseille, Aix-Marseille Université (U1), Technopôle de Château-Gombert, 13453 Marseille CEDEX 13, France
Olivier Pouliquen
Affiliation:
IUSTI-CNRS UMR 6595, Polytech-Marseille, Aix-Marseille Université (U1), Technopôle de Château-Gombert, 13453 Marseille CEDEX 13, France
Élisabeth Guazzelli
Affiliation:
IUSTI-CNRS UMR 6595, Polytech-Marseille, Aix-Marseille Université (U1), Technopôle de Château-Gombert, 13453 Marseille CEDEX 13, France
*
†Email address for correspondence: francois.boyer@polytech.univ-mrs.fr
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Abstract

We measure the second normal-stress difference in suspensions of non-Brownian neutrally buoyant rigid spheres dispersed in a Newtonian fluid. We use a method inspired by Wineman & Pipkin (Acta Mechanica, vol. 2, 1966, pp. 104–115) and Tanner (Trans. Soc. Rheol., vol. 14, 1970, pp. 483–507), which relies on the examination of the shape of the suspension free surface in a tilted trough flow. The second normal-stress difference is found to be negative and linear in shear stress. The ratio of the second normal-stress difference to shear stress increases with increasing volume fraction. A clear behavioural change exhibiting a strong (approximately linear) growth in the magnitude of this ratio with volume fraction is seen above a volume fraction of 0.22. By comparing our results with previous data obtained for the same batch of spheres by Boyer, Pouliquen & Guazzeli (J. Fluid Mech., 2011, doi:10.1017/jfm.2011.272), the ratio of the first normal-stress difference to the shear stress is estimated and its magnitude is found to be very small.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow Non-Newtonian Flows: Rheology Complex Fluids: Suspensions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 686 , 10 November 2011 , pp. 26 - 39
Copyright
Copyright © Cambridge University Press 2011

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Couturier et al. supplementary movie

Movie 1. Evolution of the free surface deflection of a suspension flowing down a tilted trough using the projection of 9 laser sheets. A characteristic steady triangular convex shape is rapidly obtained. Suspension of polystyrene spheres (having a radius a = 35 μm) in poly(ethylene glycol-ran-propylene glycol) monobutylether (with density closely matched to that of the particles ρf = 1.051 g.cm-3 and large viscosity ηf = 2.15 Pa.s at 25°C) at a volume fraction φ = 0.5. Parallel-sided channel of width W = 3 cm tilted at an angle θ = 21.3°. Movie accelerated 15x over real time (64s).

Download Couturier et al. supplementary movie(Video)
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