Scheme of the viscous resuspension problem. The top plate of the shear device is moving, as indicated by the arrow, from left to right. The system under shear adopts (a) three-phase (b), two-phase [(c) or (d)], and one-phase (e) configuration with increasing plate velocity.
Couette cell and shear experiment preparation. (a) Initially the slurry is prepared with a slight excess of immersion fluid inside the stator (radius ). (b) The rotor (radius ) is brought in contact with the sediment. The excess immersion fluid forms a ring of height between the coaxial cylinders. See Appendix A for definitions of other symbols.
Scheme of the optical setup. In this configuration, the experiment provides a view of fluorescent tracers inside a vertical plane across the Couette device.
Fluctuations of the flow and wall slip. (a) The photos are snapshots of the velocity field in a vertical plane. Note the large fluctuations of the DPIV vectors in the flow direction. (b) Time fluctuations of the horizontal component of the velocity, at different depths (, 1, and , from top to bottom), scaled to the plate velocity for and . (c) The coupling of the suspension to the upper plate fluctuates in time. The wall-slip effect is defined through the ratio, where . The coupling is very poor at small speed, but improves up to a plateau value in the high-speed regime.
Average shear flow. (a) Velocity profiles, scaled to , at constant and variable . (b) Averaged video sequences at variable and constant ( in this example) used to determine the thickness of the flowing region.
Thickness of the flowing region vs local plate velocity . (a) The graph is composed of three curves corresponding to three rotors speeds. Finite-size effects due to coupling to the outer boundary of the shear device are responsible for the decrease of at the cell periphery. (b) vs (filled symbols) and vs (open symbols), in log-log representation. The dotted straight line is the prediction of the model in the asymptotic regime [Eq. (19)], with , , , , , and .
Average shear stress (a) and average normal stress (b) vs angular velocity of the rotor in controlled shear mode (c.sh.) or controlled stress mode (c.str.) for mean particle volume fraction and gap . (c) Average normal stress vs average shear stress . The dashed line is the prediction of the model, according to Eq. (22), with , , , , , , , and . The straight line (mixed) corresponds to the asymptotic relation Eq. (23) with .
Scheme of the theoretical infinite-plate geometry. and are the tangential and normal stresses exerted by the sheared slurry upon the upper plate.
Graphical construction to derive concentration fields. (a) Shape of the master curve [Eq. (9)]. The inflexion point is inside the [0,1] physical concentration range only if is large. (b) The sample initial state, in theory, is a two-phase configuration, with a small layer (thickness ) of immersion fluid on top of a sediment . [(c)–(e)] Sequence of three-, two-, and one-phase configurations corresponding to increasing values of .
Scaled velocity fields. (a) Data recorded at constant and variable . (b) Constant and variable .
Average shear stress vs rotor velocity for pure oil filling the space between parallel plates and for , 2, 5, . The corresponding straight lines are the predictions from Eq. (A3) with and . The bold solid line indicates the dependence for the parallel-disk geometry without edge effects.
Theoretical concentration profiles (a), velocity profiles (b), and thickness of the flowing region vs the tangential stress (c) and vs the slurry boundary velocity (d), in infinite-plate geometry. Solid and dotted lines correspond to the full numerical solution and to asymptotic expressions Eqs. (15)–(20), respectively, with , , , , , , , and .
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