Figure 1

(a) Snapshots of the elastic filament driven by the slow (left) and fast (right) stroke: $N=20$, $l_p/l=2\times {10}^5$, ${\tau }_s=2\times {10}^5{k}_{B}T$, ${\varphi }_{\max }=\pi /6$, $\rho =0.0005$, and torque ratio $\alpha =4$. Here $n$ refers to the number of simulation steps. Note that the number of steps between successive snapshots is 5 times larger in the slow stroke. (b) Lateral flow profile as a function of distance from the no slip wall. The number indices refer to corresponding conformations in (a). (c) Temporal evolution of bulk solvent velocity ${\tilde{v}}_{\infty }$ over a few beating cycles. (d) Snapshots of a stiffer filament for the same parameters as in (a) but persistence length $l_p/l={10}^6$.Reuse & Permissions

Figure 2

(a) Efficiency $\eta$ vs persistence length for different torque strengths: ${\tau }_s=2\times {10}^3{k}_{B}T$ (circles), $2\times {10}^4{k}_{B}T$ (triangles), and $2\times {10}^5{k}_{B}T$ (diamonds). (b) Contour plot of efficiency $\eta$ as a function of $l_p/l$ and ${\tau }_s/k_{B}T$. The brighter, the more efficient. The linear relationship between ${\tau }_s/k_{B}T$ and $l_p/l$ for maximal efficiency is clearly seen. For all data, parameters are chosen as $\alpha =3$, ${\varphi }_{\max }=\pi /4$, and $\rho =0.001$.Reuse & Permissions

Figure 3

Contour plot of efficiency as a function of $\alpha ={\tau }_f/{\tau }_s$ and $l_p/l$ at fixed ${\tau }_s=2\times {10}^4{k}_{B}T$. The brighter, the more efficient. The optimal ratio of ${\tau }_f/{\tau }_s$ is found to be around 3. The used parameters are $\rho =0.001$ and ${\varphi }_{\max }=\pi /4$.Reuse & Permissions

Figure 4

(a) Phase difference between two cilia vs the number of beating cycles $m$ for several initial phase differences. Inset indicates phase locking in the longtime limit. The parameters are ${\tau }_s=2\times {10}^5{k}_{B}T$, $\alpha =3$, ${\varphi }_{\max }=\pi /4$, $l_p/l=2\times {10}^5$, and $\rho =0.001$. (b) Efficiency $\eta$ vs $l_p$: for one cilium per unit cell with periodic boundary ( $\Delta \varphi =0$, squares), for one cilium with open boundary (triangles), and for two cilia (diamonds) with variable $\Delta \varphi$, which is denoted by solid circles. The parameters are the same as (a) except for $\rho =0.002$.Reuse & Permissions