Thermally driven Casimir ratchet-oscillator system

We study a fluctuation-driven ratchet-oscillator system that consists of two ratchet pinions in contact with thermal baths at different temperatures. Coupling between noncontact parts of the system is mediated by the Casimir force through a thin corrugated plate. Due to mutual rectification, the two ratchets achieve directed average motion in opposite directions. We numerically probe the average velocity, the Peclet number, and the thermal efficiency of the system as functions of the effective temperatures of the thermal baths and other important dimensionless control parameters. It is found that optimal parameter values exist which maximize the directed transport rate but with very low efficiency. We expect that the obtained results will help in the design of noncontact mechanical devices in the future.

Figure 1

(a) An illustration of the Casimir ratchet-oscillator device. (b) The two thin corrugated plates with relative lateral displacement $x-y$. (c) The Casimir potential as a function of the shift $\tilde{b}=b/\lambda$.

Figure 2

Average position of the two ratchets as a function of the dimensionless time $s$ at ${\tilde{\tau }}_{1,2}=0$, $\tilde{k}=30$, $k_B{T}_1=4$, $\tilde{\gamma }=1$, $g=0.1,$ and $H/\lambda =0.1$.

Figure 3

The average velocity and the Peclet number as functions of the effective temperatures $k_B{T}_1$ at ${\tilde{\tau }}_{1,2}=0$, $\tilde{k}=30$, $\tilde{\gamma }=1$, $g=0.1,$ and $H/\lambda =0.1$.

Figure 4

The dependence of the average velocity and the Peclet number on the dimensionless spring constant $\tilde{k}$ for ${\tilde{\tau }}_{1,2}=0$, $k_B{T}_1=4$, $\tilde{\gamma }=1$, $g=0.1,$ and $H/\lambda =0.1$.

Figure 5

The dependence of the average velocity and the Peclet number on the dimensionless parameter $g$ for ${\tilde{\tau }}_{1,2}=0$, $k_B{T}_1=4$, $\tilde{\gamma }=1$, $\tilde{k}=30,$ and $H/\lambda =0.1$.

Figure 6

The dependence of the average velocity and the Peclet number on the dimensionless friction coefficient $\tilde{\gamma }$ for ${\tilde{\tau }}_{1,2}=0$, $k_B{T}_1=4$, $\tilde{k}=30$, $H/\lambda =0.1,$ and $g=0.1$.

Figure 7

The average velocity and the Peclet number as functions of the interaction magnitude $H/\lambda$ for ${\tilde{\tau }}_{1,2}=0$, $k_B{T}_1=4$, $\tilde{k}=30$, $\tilde{\gamma }=1,$ and $g=0.1$.

Figure 8

The average velocity as a function of the external loads ${\tilde{\tau }}_1$ and ${\tilde{\tau }}_2$ for $k_B{T}_1=4$, $T_1=4$, $\tilde{\gamma }=1$, $H/\lambda =0.1,$ and $g=0.1$. (a) ${\tilde{\tau }}_2=0,$ (b) ${\tilde{\tau }}_1=0$.

Figure 9

The efficiency vs the dimensionless spring constant $\tilde{k}$ for $k_B{T}_1=4$, $\tilde{\gamma }=1$, $g=0.1$, $H/\lambda =0.1,$ and different external loads ${\tilde{\tau }}_1$ and ${\tilde{\tau }}_2$.

Figure 10

The efficiency vs the parameter $g$ for $k_B{T}_1=4$, $\tilde{\gamma }=1$, $\tilde{k}=30$, $H/\lambda =0.1,$ and different external loads ${\tilde{\tau }}_1$ and ${\tilde{\tau }}_2$.

Figure 11

The efficiency vs the dimensionless friction coefficient $\tilde{\gamma }$ for $k_B{T}_1=4$, $\tilde{k}=30$, $g=0.1$, $H/\lambda =0.1,$ and different external loads ${\tilde{\tau }}_1$ and ${\tilde{\tau }}_2$.

Figure 12

The efficiency vs the interaction magnitude $H/\lambda$ for $k_B{T}_1=4$, $\tilde{k}=30$, $g=0.1$, $\tilde{\gamma }=1,$ and different external loads ${\tilde{\tau }}_1$ and ${\tilde{\tau }}_2$.

Figure 13

The efficiency vs the load ${\tilde{\tau }}_2$ for different ${\tilde{\tau }}_1$'s with $k_B{T}_1=4$, $\tilde{k}=30$, $g=0.1$, $H/\lambda =0.1,$ and $\tilde{\gamma }=1$.