Experimental study of energy exchanges between two coupled granular gases

We report on the energy exchanges between two granular gases of different densities coupled electromechanically by immersed blades attached to dc motors. Zeroing the energy flux between the two subsystems, we demonstrate that an immersed blade is a convenient way to assess the properties of the granular gases, provided that the dissipation in the motor is properly taken into account. In addition, when the two gases have different densities, the fluctuations of the energy flux are asymmetric, very intermittent, and with most probable zero flux. We show that, for weak coupling, the main features of the energy exchanges can be explained considering the fluctuations of the two subsystems.

Figure 1

Sketch of the experimental setup.

Figure 2

Sketch of the electrical circuit.

Figure 3

Probability distribution functions $P\left(e_2\right)$ for several values of $N_2$ (from dark to light red: $N_2=374$, 249, 167, 111, 74, 50, 30, and 20 beads). Curves are shifted for clarity.

Figure 4

Examples of temporal signals $e_2\left(t\right)$ for $N_2=374$ (top) and 20 (bottom) beads. Red dots represent collisions of the blade with a bead.

Figure 5

Probability distribution functions $P\left(e_2\right)$ for $N_2=20$ (dark blue) and for $N_2=374$ beads (dark red). They are fitted by Eq. (9) using $e_2=\alpha {\dot{\theta }}_2$ (light blue and light red). Curves are shifted for clarity.

Figure 6

Parameters $\mu$ (top) and $E_c$ (bottom) deduced from the fit of $P\left(e_2\right)$ to Eq. (9) as a function of $N_2$. Black line: $E_c=E_{\infty }\left(1+N_c/N_2\right)$.

Figure 7

Ratio $\tau /\left({\tau }_c{\dot{\theta }}_c\right)$ deduced from Eq. (9) as a function of $N_2$.

Figure 8

Probability distribution functions $\mathcal{P}\left(\mathrm{\Phi }\right)$ for several values of $N_2$ (from dark to light red: $N_2=374$, 249, 167, 111, 74, 50, 30, and 20 beads). Curves are shifted for clarity.

Figure 9

Skewness ($S_{\mathrm{\Phi }}$, blue circles) and kurtosis ($K_{\mathrm{\Phi }}$, red squares) of $P\left(\mathrm{\Phi }\right)$ as a function of $N_2$.

Figure 10

Distribution $\mathcal{P}\left(\mathrm{\Phi }\right)$ (dark blue) compared to its estimate from Eqs. (10) (light blue) $[N_1=374$ – $N_2=20]$.