Fall of a large sphere in a suspension of small fluidized particles

The investigation of the fall of a sphere at finite Reynolds number in a concentrated suspension of small fluidized particles leads to unexpected results. By analyzing the drag force, it is shown that the average surface stress on the sphere is independent of the size of the sphere. It is proportional to an effective viscosity determined from the sedimentation velocity of the particles multiplied by the velocity of the sphere and divided by the size of the particles. These results question the role of concentration inhomogeneities that occur on a large scale in the overall flow around a moving obstacle and on a small scale near its surface.

Figure 1

Scheme of the experimental setup.

Figure 2

Mixture effective viscosity defined from the fluidization velocity of the suspension. Symbols: measurements. Line: model from [7], taking $\mathcal{F}\left(\frac{{\mathrm{\Phi }}_s}{{\mathrm{\Phi }}_{\mathrm{pack}}}\right)=\frac{1}{(e^{-3}+0.08)}[e^{-3(1-\frac{{\mathrm{\Phi }}_s}{{\mathrm{\Phi }}_{\mathrm{pack}}})}+0.08{(1-\frac{{\mathrm{\Phi }}_s}{{\mathrm{\Phi }}_{\mathrm{pack}}})}^{-2/3}]$.

Figure 3

Relative sphere velocity versus particle concentration.

Figure 4

Drag coefficient of the sphere versus the Reynolds number (values of $k$ in Fig. 5).

Figure 5

Coefficient $k$ against $\frac{D}{d}$.