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Wall forces on a sphere in a rotating liquid-filled cylinder
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View: Figures


Image of FIG. 1.
FIG. 1.

Forces acting on a particle: the added mass force, the drag force, the lift force, the gravity force or body force, the force due to acceleration of the flow, and the wall repulsive force.

Image of FIG. 2.
FIG. 2.

Experimental setup. 1. Laser, 2. Drum, 3. Drum controller, 4. Camera, 5. Camera controller.

Image of FIG. 3.
FIG. 3.

Solid-body rotational flow at a drum frequency of 0.60 Hz. (a) A snapshot of the PIV tracer particles. (b) Flow field inside the rotating drum. The scratched region is highlighted in gray color. The red line shows the position of the velocities shown in (c). (c) Velocity vs. position along a horizontal line shown in (b). The markers (red online) show the measured velocities and the black line is the theoretical velocity of solid body rotating flow.

Image of FIG. 4.
FIG. 4.

Four regimes of a heavy particle trajectory: (1) Fixed-point regime, (2) cascading regime, (3) fixed solid body rotation regime, and (4) suspension regime.

Image of FIG. 5.
FIG. 5.

Particle position of a 7 mm polystyrene particle in a drum for frequency 0.07–0.11 Hz. The cross markers show the average positions for each trajectory.

Image of FIG. 6.
FIG. 6.

Images of a particle slightly heavier than the fluid with black and white texture in a drum. (a) Snapshots of a particle in orbital motion. (b) Zoomed image for a particle close to the wall.

Image of FIG. 7.
FIG. 7.

The equilibrium radius vector , the momentary position of the sphere , and the particle velocity . The particle turns around with momentary angular velocity . The dashed black line represents the particle circular orbit. The cross marker shows the equilibrium point.

Image of FIG. 8.
FIG. 8.

Comparison between experimental results and numerical solution from Eq. ( ) for (a) radial center position and (b) radius of orbital motions as a function of Reynolds number (correspond to the drum frequency 0.07–0.11 Hz).

Image of FIG. 9.
FIG. 9.

Paths reproduced by Eq. (5) for the drum frequency 0.07–0.11 Hz.

Image of FIG. 10.
FIG. 10.

Magnitude of the particle velocity vs time normalized by the drum time cycle.

Image of FIG. 11.
FIG. 11.

The absolute angular rotation of the sphere in a solid body rotating flow with = 0.07 Hz for one period of the drum.

Image of FIG. 12.
FIG. 12.

The result of the flow field around a 7 mm particle in a drum at = 0.07 Hz using particle image velocimetry. (a) Flow field and (b) Velocities vs. positions along the lines shown in the left panel.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Wall forces on a sphere in a rotating liquid-filled cylinder