Transport and diffusion properties of Brownian particles powered by a rotating wheel

Diffusion and rectification of Brownian particles powered by a rotating wheel are numerically investigated in a two-dimensional channel. The nonequilibrium driving comes from the rotating wheel, which can break thermodynamical equilibrium and induce the directed transport in an asymmetric potential. It is found that the direction of the transport along the potential is determined by the asymmetry of the potential and the position of the wheel. The average velocity is a peaked function of the angular speed (or the diffusion coefficient) and the position of the peak shifts to large angular speed (or diffusion coefficient) when the diffusion coefficient (or the angular speed) increases. There exists an optimal angular speed (or diffusion coefficient) at which the effective diffusion coefficient takes its maximal value. Remarkably, the giant acceleration of diffusion is observed by suitably adjusting the system parameters. The parameters corresponding to the maximum effective diffusion coefficient are not the same as the parameters at which average velocity is maximum.

Figure 1

(a) Schematic of the rotating wheel motor: Brownian particles (blue disks) driven by the rotating wheel with angular speed $\mathrm{\Omega }$ and moving in a straight periodic channel with width $L_y$ and period $L_x$. Periodic boundary conditions imposed in the $x$ direction and hard wall boundary conditions in the $y$ direction. The wheel is composed of three paddles, and each paddle consists of $n_p$ paddle particles (yellow disks). The wheel is centered at the point $(x_c,y_c)$ and the angle between paddles is $2\pi /3$.

Figure 2

The profile of the $x$ direction in the potential $V\left(x\right)$ described in Eq. (3) for different values of the parameter $\mathrm{\Delta }$. The left side of the potential is steep for $\mathrm{\Delta }<0$ and the right side is steep for $\mathrm{\Delta }>0$.

Figure 3

Average velocity $V_s$ as a function of the asymmetric parameter $\mathrm{\Delta }$. (a) For different values of $\mathrm{\Omega }$ at $D_0=1.0$. (b) For different values of $D_0$ at $\mathrm{\Omega }=4.0$.

Figure 4

(a) Average velocity $V_x$ as a function of the angular speed $\mathrm{\Omega }$ for different values of $D_0$ at $\mathrm{\Delta }=-0.5$. (b), (c) Scaled effective diffusion coefficient $D_{\mathrm{eff}}$ as a function of the angular speed $\mathrm{\Omega }$ for different values of $D_0$ at $\mathrm{\Delta }=-0.5$.

Figure 5

(a) Average velocity $V_x$ as a function of the diffusion coefficient $D_0$ for different values of $\mathrm{\Omega }$ at $\mathrm{\Delta }=-0.5$. (b) Scaled effective diffusion coefficient $D_{\mathrm{eff}}$ as a function of the diffusion coefficient $D_0$ for different values of $\mathrm{\Omega }$ at $\mathrm{\Delta }=-0.5$.

Figure 6

Contour plots of the average velocity $V_x$ as a function of the system parameters $\mathrm{\Omega }$ and $D_0$ at $\mathrm{\Delta }=-0.5$.

Figure 7

(a) Average velocity $V_x$ as a function of the packing fraction $\varphi$ at $\mathrm{\Delta }=-0.5$. (b) Scaled effective diffusion coefficient $D_{\mathrm{eff}}$ as a function the packing fraction $\varphi$ at $\mathrm{\Delta }=-0.5$.

Figure 8

(a) Average velocity $V_x$ as a function of the length $L_y$ for different values of $D_0$ at $\mathrm{\Delta }=-0.5$ and $\mathrm{\Omega }=4.0$. (b) Average velocity $V_x$ as a function of the stiffness constant $k_1$ at $\mathrm{\Delta }=-0.5$. (c) Average velocity $V_x$ as a function of $x_c$ at $\mathrm{\Omega }=4.0$ for different values of $\mathrm{\Delta }$.

Figure 9

Average velocity $V_x$ ($V_y$) as a function of the asymmetric parameter $\mathrm{\Delta }$ for both clockwise ($\mathrm{\Omega }<0$) and counterclockwise ($\mathrm{\Omega }>0$) cases at $D_0=1.0$.