Normal stresses in concentrated non-Brownian suspensions

Abstract

International audienceWe 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, and , 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, is measured to be negative but 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, , the contribution of the particles to the normal stress 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

Rheology of sheared suspensions of rough frictional particles

“…Even though our simulations with frictional particles are closer to some experimental results from the literature, they are not likely to explain all of them. Although the values of |N 1 | in the core flow are smaller, N 1 remains negative unlike some measurements from Couturier et al (2011) and Dbouk et al (2013) where N 1 is about zero or even positive. Friction contributes partly -but not wholly -to the smaller experimental values of |N 1 |.…”

“…The only difference between the frictionless and frictional cases lies in the contact contribution which significantly increases with friction. Another interesting result is that the hydrodynamic contribution to viscosity ⌘ h remains very close to the high-frequency vis- ) and Dbouk et al (2013). Non-dimensional roughness is ✏r=5.10 −3 .…”

“…By studying the deformation of the free surface of a suspension flowing in a narrow inclined channel, Couturier et al (2011) concluded that N 1 was very small compared to N 2 and within the experimental uncertainty, they were unable to determine the sign of N 1 . Likewise, a detailed experimental study by Dbouk et al (2013) using a parallel-plate geometry has found this time that N 1 is positive over the entire range of volume fraction investigated 0.2  φ  0.47. The value of N 2 however remains as in the other studies.…”

“…Figure 9 presents the φ-dependence of the suspensions relative viscosity ⌘ r for different friction coefficients µ d . A number of experimental results by Zarraga et al (2000) and Dbouk et al (2013) are also shown. For frictionless particles (µ d =0), the agreement is moderate with predicted viscosities systematically lower than experimental results.…”

“…From a more fundamental viewpoint however, the study of normal stresses is essential. Furthermore, there exist only very scarce experimental data on normal stresses in suspensions (Zarraga et al 2000;Dbouk et al 2013;Couturier et al 2011;Boyer et al 2011b;Garland et al 2012). This section considers the role of friction on normal stresses and comparisons with experiments will be provided in the forthcoming sections.…”