Anomalous Sinking of Spheres due to Local Fluidization of Apparently Fixed Powder Beds

The sinking of an intruder sphere into a powder bed in the apparently fixed bed regime exhibits complex behavior in the sinking rate and the final depth when the sphere density is close to the powder bed density. Evidence is adduced that the intruder sphere locally fluidizes the apparently fixed powder bed, allowing the formation of voids and percolation bubbles that facilitates spheres to sink slower but deeper than expected. By adjusting the air injection rate and the sphere-to-powder bed density ratio, this phenomenon provides the basis of a sensitive large particle separation mechanism.

Figure 1

Measured pressure drop, $\mathrm{\Delta }P$, as a function of the air injection superficial velocity, $u_0$ (volumetric rate/container cross-sectional area). The minimum fluidization velocity, $u_{\mathrm{mf}}$, marks the transition between the linear pressure variation of the apparently fixed bed regime and the constant pressure fluidized powder bed regime. Sphere sinking experiments were conducted at around $u_0/u_{\mathrm{mf}}\sim 1$. Schematic of the apparatus used to measure the sinking of a sphere ($D_{\text{sphere}}=30\mathrm{mm}$) in a cylindrical container (diam, 150 mm) filled to a height of 300 or 150 mm with glass beads (diam, 0.21–0.25 mm) at the powder bed density ${\rho }_{\text{bed}}=1.53\mathrm{g}/{\mathrm{cm}}^3$; see Ref. [18] for details.

Figure 2

(a) Variation on a logarithmic time scale of the depth, $h$, of sinking spheres scaled by the sphere diameter in the apparently fixed bed regime: $u_0/u_{\mathrm{mf}}=0.95$ at different sphere densities. See the Supplemental Material [18] for a video visualization of the comparative sinking rate. (b) As in (a), for $0.85\le {\rho }_{\text{sphere}}/{\rho }_{\text{bed}}\le 1.31$. (c) Variation of the final depth, $h_{\text{final}}$, of the sunken sphere with scaled sphere density. The bottom of the 300 mm deep powder bed is at $h/D_{\text{sphere}}=10$. The scale for $h$ increases downwards.

Figure 3

(a) Variation of the final depth, $h_{\text{final}}$, of a sunken sphere scaled by the bed depth, $h_{\text{bed}}$, with a sphere density, ${\rho }_{\text{sphere}}/{\rho }_{\text{bed}}$, at three superficial velocities at or just below $u_0/u_{\mathrm{mf}}=1$, in the apparently fixed bed regime. (b) Variation of the final depth, $h_{\text{final}}$, of the sunken sphere (the open symbols, left-hand axis) and the pressure drop, $\mathrm{\Delta }P$ (the solid symbols, right-hand axis), with superficial velocity, $u_0/u_{\mathrm{mf}}$, at sphere density ${\rho }_{\text{sphere}}/{\rho }_{\text{bed}}=0.98$. The powder bed depth is 150 mm.

Figure 4

Photos of the surface of the powder bed as spheres of different densities begin to sink in the experiments depicted in Fig. 2. See the Supplemental Material for corresponding videos [18].