Brownian Ratchet in a Thermal Bath Driven by Coulomb Friction

The rectification of unbiased fluctuations, also known as the ratchet effect, is normally obtained under statistical nonequilibrium conditions. Here we propose a new ratchet mechanism where a thermal bath solicits the random rotation of an asymmetric wheel, which is also subject to Coulomb friction due to solid-on-solid contacts. Numerical simulations and analytical calculations demonstrate a net drift induced by friction. If the thermal bath is replaced by a granular gas, the well-known granular ratchet effect also intervenes, becoming dominant at high collision rates. For our chosen wheel shape the granular effect acts in the opposite direction with respect to the friction-induced torque, resulting in the inversion of the ratchet direction as the collision rate increases. We have realized a new granular ratchet experiment where both these ratchet effects are observed, as well as the predicted inversion at their crossover. Our discovery paves the way to the realization of micro and submicrometer Brownian motors in an equilibrium fluid, based purely upon nanofriction.

Figure 1

(a) Sketch of the model, front view. (b) Top view, with explanation of quantities used in the text for a generic-shaped rotator. (c) Top view, with specific shapes used in the simulations and in the experiment.

Figure 2

Simulations under the assumption of molecular chaos. The rescaled average angular velocity $⟨\Omega ⟩$ is shown as a function of ${\beta }^{-1}$. Theoretical expectations in the FCL and RCL are marked by dashed lines. The lower inset zooms in the RCL region. Simulations are performed using shapes and dimensions of Fig. 1c, $\Delta =10$, ${\gamma }_a=0$, $R_I/ϵ={10}^3$, and $v_0=100$ in arbitrary units (varying $n\Sigma$ to obtain a variation of ${\beta }^{-1}$).

Figure 3

Real experiment. (a) Experimental setup. (b) The angular position of the rotator as a function of time, highlighting the ratchet effect for the asymmetric rotator. The inset shows an enlargement (10 min) extracted from a asymmetric (right) experiment. For these experiments the value of maximum acceleration, normalized by gravity, is 13.

Figure 4

Real experiment. Plot of the rescaled angular velocity of the rotator, $⟨\Omega ⟩=\frac{R_I}{ϵv_0}⟨\omega ⟩$, averaged on an 8-h run, as a function of ${\beta }^{-1}$ which estimates the ratio of time scales $\frac{{\tau }_{\Delta }}{{\tau }_c}$. The main plot shows the region where a maximum and a current inversion are observed for the asymmetric rotator. The inset sums up all the results, highlighting the behavior for large ${\beta }^{-1}$. Experiments are performed with maximum shaker acceleration varying in the range from 5 to 20 in gravity units.