The role of tap duration for the steady state density of vibrated granular media

TL;DR

This study investigates how tap duration influences the steady state density of vibrated granular media, revealing that the density depends on the ratio A/T and challenging the conventional focus on peak acceleration as the key control parameter.

Contribution

The paper demonstrates that the relevant control parameter for granular compaction under sinusoidal tapping is A/T, not peak acceleration, and provides a unified scaling approach for density data.

Findings

Density depends on A/T ratio.

Scaling collapse of data when plotted against A/T.

Switching states with same density shows negligible hysteresis.

Abstract

We revisit the problem of compaction of a column of granular matter exposed to discrete taps. We accurately control the vertical motion of the column, which allows us to vary the duration T and the amplitude A of single-cycle sinusoidal taps independently. We find that the density of the material at the reversible branch depends both on A and T. By comparing the densities on the reversible branches obtained for a range of values of T, we find that we can collapse all data when plotted as function of A/T, which scales similar to both the liftoff velocity and the time of flight of the packing. We further show that switching between states obtained for different A and T, but chosen such that their densities on the reversible branches match, does not lead to appreciable hysteresis. We conclude that the appropriate control parameter for sinusoidal tapping is not the peak acceleration \Gamma \sim A/T^2, as is usually assumed, but rather \Gamma T \sim A/T.