Parametric study of the vibration-induced repulsion or attraction force on a particle in a viscous fluid cell

Experiments and three-dimensional direct numerical simulations were performed to investigate the effects of physical parameters on the repulsion or attraction force affecting the motion of a particle oscillating near a solid wall of a fluid cell under microgravity. The following physical parameters were investigated: fluid cell amplitude, fluid and particle densities, angular frequency of the cell vibration, initial distance between the particle centroid and the closest cell wall, particle radius, and dynamic viscosity. Based on the simulations, a nondimensional relation was developed to relate those physical parameters to the repulsion or attraction force affecting the particle. The relation shows that the repulsion or attraction force is increased by the increase in the cell vibration amplitude and frequency and also the force direction would change from attraction to repulsion above a threshold fluid viscosity. Relations to other physical parameters were also studied and are reported. This paper follows our previous work on the physical mechanism of observed repulsion force on a particle in a viscous fluid cell [M. Saadatmand and M. Kawaji, Phys. Rev. E 88, 023019 (2013)].

Figure 1

Experimental setup and side view of the fluid cell.

Figure 2

Top view of the fluid cell with the cell walls labeled.

Figure 3

Transverse particle displacement from a neutral position as a function of cell frequency and amplitude for 1000-cSt silicone oil and a steel particle of 4.0 mm diameter suspended by a synthetic silk thread. For all cases δ was 0.85 mm.

Figure 4

Variation of particle amplitude with cell amplitude for 1000-cSt fluid and three different cell amplitudes (with a particle diameter of 4.0 mm, synthetic silk thread, and δ = 0.85 mm).

Figure 5

Force balance around the particle.

Figure 6

Attraction force as a function of cell frequency obtained from experiments and simulations for a steel particle of 12.7 mm diameter suspended in water (δ = 0.82 mm).

Figure 7

Repulsion force as a function of cell frequency obtained from experiments (closed symbols) and simulations (open symbols) for a steel particle of 4.0 mm diameter suspended in 1000-cSt silicone oil (δ = 0.85 mm).

Figure 8

Dimensionless attraction force as a function of dimensionless cell amplitude; the slope of the line is 2.0.

Figure 9

Attraction force as a function of ${[(1-\tilde{\rho })/(2+\tilde{\rho })]}^2$ for the change in the solid density.

Figure 10

Dimensionless attraction force as a function of $\tilde{H}$; the slope of the dashed line is −3.0.

Figure 11

Dimensionless attraction or repulsion force as a function of $\tilde{S}={\rho }_f\omega R_0^2/\mu$.

Figure 12

Attraction force as a function of dimensionless cell frequency.

Figure 13

Attraction force as a function of particle radius.

Figure 14

Comparison of predicted repulsion or attraction force, Fy, in symbols with Eq. (15) shown by a solid line.