Particle Mixing and Volumetric Expansion in a Vibrated Granular Bed

The present experiments are an investigation of the expansion and mixing that occur in a horizontal bed of particles subjected to vibrational accelerations in the direction parallel to gravity. The particles are colored-glass balls of uniform size; three different bed heights are examined of 6, 9, and 12 particle diameters. The vibrational frequency and amplitude are controlled separately to cover a range of acceleration levels from 1 to 5.5 times gravitational acceleration. The expansion results show that above a critical frequency, the bed begins to expand and the bed solid fraction decreases. This result is independent of the vibrational amplitude. Above a second critical frequency, the thickest beds show a further decrease in solid fraction; the minimum value of solid fraction for all bed heights is approximately 0.21 ± 0.03. The mixing results indicate that the mixing times decrease significantly with the expansion of the bed. However, the mixing times are greater as the bed depth increases. Unlike the expansion results, the mixing times depend on the amplitude of the vibration. A simple analysis of the flow is performed using a self-diffusion coefficient developed from dense-gas kinetic theory. The analysis qualitatively agrees with the experiments for the largest vibrational velocities and for the thinnest beds.