Cooling of a Tapped Granular Column

We present the results of a discrete element investigation of the cooling of a tapped column of uniform, inelastic spherical particles ($d)$ as it evolves to a state of zero kinetic energy. A linear loading-unloading soft contact model is employed, while tapping is simulated by applying a half-sine pulse of amplitude $a$/$d$ and frequency $f$ to a rigid floor supporting the column. For sufficiently energetic taps, the column dilates and then contracts over a time scale $t_{s}$, which depends on the number of particles $N$, restitution coefficient $e$, as well as tap parameters ($a$/$d$, $f)$. Simulation data for (\textit{1} $\le N \le $ \textit{50}) with other parameters being held constant suggested that a time-averaged collision frequency $f_{\mathrm{c}}$ scaled with $N$. Values of $t_{s}$, determined by identifying the instant when the kinetic energy thereafter remained less than \textit{0.001{\%} }of its maximum value, were well-correlated with the form $\alpha (e)N^{-1} + \beta (e)$. Lastly, simulations were in good agreement with physical considerations, suggesting that $t_{s}$ should scale with (1 -- $e^{2})^{-1}$ and inversely with $f_{\mathrm{c}}$.