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Normal stresses in concentrated non-Brownian suspensions

Published online by Cambridge University Press:  09 January 2013

T. Dbouk ,
L. Lobry  and
E. Lemaire
T. Dbouk
Affiliation:
Laboratoire de Physique de la Matière Condensée (LPMC, UMR 6622), Parc Valrose, 06108 Nice CEDEX 2
L. Lobry
Affiliation:
Laboratoire de Physique de la Matière Condensée (LPMC, UMR 6622), Parc Valrose, 06108 Nice CEDEX 2
E. Lemaire*
Affiliation:
Laboratoire de Physique de la Matière Condensée (LPMC, UMR 6622), Parc Valrose, 06108 Nice CEDEX 2
*
†Email address for correspondence: [email protected]
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Abstract

We present an experimental approach used to measure both normal stress differences and the particle phase contribution to the normal stresses in suspensions of non-Brownian hard spheres. The methodology consists of measuring the radial profile of the normal stress along the velocity gradient direction in a torsional flow between two parallel discs. The values of the first and the second normal stress differences, ${N}_{1} $ and ${N}_{2} $, are deduced from the measurement of the slope and of the origin ordinate. The measurements are carried out for a wide range of particle volume fractions (between 0.2 and 0.5). As expected, ${N}_{2} $ is measured to be negative but ${N}_{1} $ is found to be positive. We discuss the validity of the method and present numerous tests that have been carried out in order to validate our results. The experimental setup also allows the pore pressure to be measured. Then, subtracting the pore pressure from the total stress, ${\mbrm{\Sigma} }_{\mathbf{22} } $, the contribution of the particles to the normal stress ${ \mbrm{\Sigma} }_{\mathbf{22} }^{\mathbi{p}} $ is obtained. Most of our results compare well with the different experimental and numerical data present in the literature. In particular, our results show that the magnitude of the particle stress tensor component and their dependence on the particle volume fraction used in the suspension model balance proposed by Morris & Boulay (J. Rheol., vol. 43, 1999, p. 1213) are suitable.

JFM classification

Non-Newtonian Flows: Non-Newtonian Flows Non-Newtonian Flows: Rheology Complex Fluids: Suspensions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 715 , 25 January 2013 , pp. 239 - 272
Copyright
©2013 Cambridge University Press

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