Normal stresses in concentrated non-Brownian suspensions

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.