High-resolution one-dimensional spatio-temporal analysis of compaction in vibrated granular material

Abstract

Shaking a granular material results to compaction. This process translates to an increase of packing fraction affecting further granular compressibility and flow. We did numerical experiments on the compaction properties of a monodispersed spherical granular material under varied sinusoidal vertical shaking for different amplitude A and frequency f. We measured the local density profile of the granular material as a function of position along the confined granular column as compaction progresses. Fitting the simulation data to Knight's logarithmic compaction law yielded final packing fractions ρ_f and change in packing fractions Δρ_∞, allowing us to map the Carr Index (a measure of compressibility) against A and f. Our results, consistent with prior experimental work but with better spatio-temporal resolution, showed packing fraction increasing logarithmically over shaking time. The resulting A-f map indicates higher compressibility at higher amplitudes and lower frequencies. Furthermore, this high-resolution approach confirms previous studies, suggesting that future investigations of other parameters in the model will yield better insights into this important industrial process.