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We present an extensive numerical study of the time irreversibility of thedynamics of heavy inertial particles in three-dimensional, statisticallyhomogeneous and isotropic turbulent flows. We show that the probability densityfunction (PDF) of the increment, $W(\tau)$, of a particle's energy over atime-scale $\tau$ is non-Gaussian, and skewed towards negative values. Thisimplies that, on average, particles gain energy over a period of time that islonger than the duration over which they lose energy. We call this$\textit{slow gain}$ and $\textit{fast loss}$. We find that the third moment of$W(\tau)$ scales as $\tau^3$, for small values of $\tau$. We show that the PDFof power-input $p$ is negatively skewed too; we use this skewness ${\rm Ir}$ asa measure of the time-irreversibility and we demonstrate that it increasessharply with the Stokes number ${\rm St}$, for small ${\rm St}$; this increaseslows down at ${\rm St} \simeq 1$. Furthermore, we obtain the PDFs of $t^+$ and$t^-$, the times over which $p$ has, respectively, positive or negative signs,i.e., the particle gains or loses energy. We obtain from these PDFs a directand natural quantification of the the slow-gain and fast-loss of the particles,because these PDFs possess exponential tails, whence we infer thecharacteristic loss and gain times $t_{\rm loss}$ and $t_{\rm gain}$,respectively; and we obtain $t_{\rm loss} < t_{\rm gain}$, for all the cases wehave considered. Finally, we show that the slow-gain in energy of the particlesis equally likely in vortical or strain-dominated regions of the flow; incontrast, the fast-loss of energy occurs with greater probability in the latterthan in the former.

Heavy inertial particles in turbulent flows gain energy slowly but lose it rapidly