Brownian motor in a granular medium

In this work we experimentally study the behavior of a freely rotating asymmetric probe immersed in a vibrated granular medium. For a wide variety of vibration conditions the probe exhibits a steady rotation whose direction is constant with respect to the asymmetry. By changing the vibration amplitude and by filtering the noise in different frequency bands we show that the velocity of rotation depends not only on the RMS acceleration $\Gamma$, but also on the amount of energy provided to two separate frequency bands, which are revealed to be important for the dynamics of the granular medium: The first band governs the transfer of energy from the grains to the probe, and the second affects the dynamics by altering the viscosity of the vibro-fluidized material.

Figure 1

Example of the symmetric and asymmetric probes used (a). The probe is supported vertically by stops that bear on fixed teflon sleeves (b) allowing free rotation and is inserted into a beaker (c) containing the beads. The beaker is vibrated by a shaker (d) (Bruel and Kjaer type 4809), and the instantaneous angular position of the probe is registered by a rotary encoder (e) with resolution $1/{500}^{°}$.

Figure 2

Probe average velocity as a function of the shaking acceleration for the $\text{two}-$ and four-teeth asymmetric probes (numbered 1 to 4 as in Fig. 1). The vibration signal is white noise filtered in the range 15–300 Hz. Inset: Average rotation velocity $\omega$ as a function of the immersion depth $H$ of the probe at $\Gamma =2$. At $H=3$ cm the probe is fully immersed in the medium.

Figure 3

The asymptotic value of the probe velocity (i.e., $\langle \omega \rangle$ at $\Gamma =4$) while varying the lower cutoff $f_1$ of the bandpass filter from $15$ to $60$ Hz, necessitating an increase in the filter amplitude in order to maintain a constant $\Gamma$. The mean velocity decreases approximately proportional to $f_1$ with a step between $30$ and $40$ Hz, coincident with an absorption peak previously observed in the apparatus’s response function [19].

Figure 4

The value of the probe velocity (measured at $\Gamma =4$) while varying the upper cutoff $f_2$ of the bandpass filter. This was performed both with a single band, maintaining the overall signal energy by decreasing the amplitude as appropriate, and with a double band at constant amplitude (see inset). In the first case, the velocity decreases (circles and black line) displaying a roughly linear behavior with respect to the amplitude (triangles and green line). In the second case, increasing sevenfold the energy in the upper band produces only a slight increase in the mean probe velocity (crosses and blue line); this is in contrast to the result in Fig. 3 where a reduction of approximately 15% resulted in a 75% reduction in the velocity.