ABSTRACT
The experimental set-up mainly consists in a HeleShaw cell composed of two glass plates of length L = 130 cm and height H = 20 cm separated by a small gap b = 2 mm (Fig. 1). The cell is partially filled with sieved glass beads (∼10 cm), of mean diameter d and density ρs = 2.5 103 kg/m3. The beads are fully immersed in water and a hydrodynamic continuous flow is imposed through the cell without any free surface. The cell can rotate in the vertical plane parallel to the two glass plates. The tilt angle β between the horizontal and the cell longitudinal axis can be modified continuously in the range [−60◦, +60◦]. By convention β is chosen positive when water flows uphill and negative when it flows downhill, the horizontal situation then corresponds to β= 0. In such a narrow flume, as far as the flow remains laminar, the velocity profile of the water current is parabolic across the gap b. The gap averaged velocity U is constant except near the upper wall or close to the granular surface. If we
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neglect the fact that the bed is rough at the grain scale and that the bed is porous which means that velocity is not exactly zero at the bed surface, this mean velocityU goes exponentially to zero at the bed surface with a characteristic length scale equal to the cell thickness b (Gondret et al., 1997). The shear close to the interface then writes γ˙ ≈ 3.26 U/b (see Gondret et al., 1997). These results are valid as long as the flow remains laminar in the cell i.e. that the flow Reynolds number Reb = ρlUb/η based on the mean fluid velocity U and the cell gap size b, remains below 900. This is the case in the present study as Reb < 500. However if this Reynolds number is important for determining if the bulk flow is laminar or turbulent, it is not the relevant parameter at the grain scale. More appropriate is the particle Reynolds number Red = ρlu0d/η based on the grain diameter d and on the typical velocity of the fluid u0 = γ˙d/2 at the center of a grain lying on the granular surface estimated at the height d/2 over the bed. In the literature concerned with sediment transport, the classical dimensionless number in use is the Shields number (Shields, 1936). This parameter is the ratio between tangential and normal stresses acting on a grain and may then be written as: θ = ηγ˙/ρgd, where ρ= ρs − ρl (indices s and l stand for solid and liquid).
