Flow of Wet Granular Materials

N. Huang, G. Ovarlez, F. Bertrand, S. Rodts, P. Coussot, and Daniel Bonn

Phys. Rev. Lett. 94, 028301 – Published 18 January 2005

Abstract

The transition from frictional to lubricated flows of a dense suspension of non-Brownian particles is studied. The pertinent parameter characterizing this transition is the Leighton number $L e = \frac{η_{s} \dot{γ}}{σ}$ , the ratio of lubrication to frictional forces. Le defines a critical shear rate below which no steady flow without localization exists. In the frictional regime the shear flow is localized. The lubricated regime is not simply viscous: the ratio of shear to normal stresses remains constant and the velocity profile has a universal form in both frictional and lubricated regimes. Finally, a discrepancy between local and global measurements of viscosity is identified, which suggests inhomogeneity of the material under flow.

Received 2 June 2004

DOI:https://doi.org/10.1103/PhysRevLett.94.028301

Authors & Affiliations

N. Huang¹, G. Ovarlez², F. Bertrand², S. Rodts², P. Coussot², and Daniel Bonn^1,3

¹Laboratoire de Physique Statistique, UMR 8550 CNRS, École Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France*
²Laboratoire des Matériaux et Structures du Génie Civil, UMR 113 LCPC-ENPC-CNRS, 2 allée Kepler, 77420 Champs-sur-Marne, France
³Van der Waals-Zeeman Institute, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, the Netherlands

^*Associated with University Paris 6 and University Paris 7, France.

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Vol. 94, Iss. 2 — 21 January 2005

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Images

Figure 1
(a) Viscosity bifurcation: under an imposed stress the viscosity either grows in time or decreases; therefore the steady-state viscosity jumps to infinity at a critical stress. This allows us to define both the critical stress and the critical shear rate. Before each experiment, the material is presheared during 30 s at $30 s^{- 1}$ to obtain a reproducible initial state. (b) Flow curve (shear stress versus shear rate) for $20 m P a s$ silicone oil, both at an imposed macroscopic shear stress and shear rate. The shaded area is the statistical error bar.Reuse & Permissions
Figure 2
Critical shear rate versus interstitial fluid viscosity, for polystyrene beads in a Newtonian liquid. The line is a power-law fit to the isodensity values with a slope of $- 0.99 \pm 0.10$ .Reuse & Permissions
Figure 3
Shear/normal stresses ratio $σ / N_{1}$ as a function of the shear rate for polystyrene beads in $20 m P a s$ silicone oil (solid volume fraction: 58%), at imposed shear rate. Both plates are covered with sand paper to avoid wall slip. The shaded area is the statistical error bar. The horizontal line appears off center because of the logarithmic scale.Reuse & Permissions
Figure 4
Velocity rescaled with the velocity of the inner cylinder (inner cylinder radius $R_{i} = 4.15 c m$ , outer cylinder radius $R_{e} = 6 c m$ , height 11 cm; we again use the $20 m P a s$ Rhodorsil silicone oil). For technical reasons, $V_{i}$ can be varied either between 0.01 and $3.91 c m / s$ or between 0.43 and $43.5 c m / s$ . As in the macroscopic rheology experiments, we preshear the material at a rotational speed $V_{i} = 43.5 c m / s$ during 30 s. For the low velocity setup, we preshear the material at the maximum possible rotational speed $V_{i}$ , i.e., $3.91 c m / s$ . The rough inner cylinder is driven at a rotational velocity $V_{i}$ ranging between 0.013 and $43.5 c m / s$ , yielding overall shear rates between 0.006 and $20.9 s^{- 1}$ , the critical shear rate $\dot{γ_{c}}$ being $0.4 \pm 0.1 s^{- 1}$ (or $V_{c} = 1.04 \pm 0.26 c m / s$ ).Reuse & Permissions
Figure 5
Velocity profiles measured in a Couette geometry. We plot $V / V_{i}$ versus $(R - R_{i}) / d_{c} (V_{i})$ , where $R_{i}$ is the inner cylinder radius and $d_{c}$ an adjustable parameter; we also plot two velocity profiles extracted from 18 for the shearing of a dry granular material (1 mm mustard grains) in a Couette geometry ( $R_{i} = 3 c m$ , $R_{e} = 6 c m$ ). The line is an exponential fit: $V / V_{i} = e^{- 5.6 (R - R_{i}) / d_{c} (V_{i})}$ ; the dotted line is for a power-law fluid fit with exponent $n = 0.13$ . Inset: $d_{c}$ versus $V_{i}$ for a $3.91 c m / s$ preshear (open triangles) and a $43.5 c m / s$ preshear (squares).Reuse & Permissions
Figure 6
Stress versus shear rate calculated from the velocity profiles for different rotational velocities and measured macroscopically [same data as Fig. 1b].Reuse & Permissions

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