Migration of active rings in porous media

Inspired by how the shape deformations in active organisms help them to migrate through disordered porous environments, we simulate active ring polymers in two-dimensional random porous media. Flexible and inextensible active ring polymers navigate smoothly through the disordered media. In contrast, semiflexible rings undergo transient trapping inside the pore space; the degree of trapping is inversely correlated with the increase in activity. We discover that flexible rings swell while inextensible and semiflexible rings monotonically shrink upon increasing the activity. Together, our findings identify the optimal migration of active ring polymers through porous media.

Figure 1

(a) A snapshot of active ring polymer in porous media and the schematic sketch of active ring polymer. Polymer is regarded as beads connected by springs. (b) A representative trajectory of the active ring polymer in the porous medium. The magenta arrows represent ring conformations corresponding to different frames in the trajectory.

Figure 2

Log-log plot of $\langle \overline{\mathrm{\Delta }{r}^2\left(\tau \right)}\rangle \text{vs}\tau$ of the passive tracer particle in different porous media.

Figure 3

The COM trajectory, log-log plot of $\langle \overline{\mathrm{\Delta }{r}_c^2\left(\tau \right)}\rangle \text{vs}\tau$, and log-linear plot of $\alpha \left(\tau \right)\text{vs}\tau$ of the ring subjected to different $F_a$ for flexible [(a), (b), and (c)], inextensible [(d), (e), and (f)], and semiflexible [(g), (h), and (i)] ring polymers, respectively, in the porous medium with $\xi =6.92$. For each time interval $\tau$, the error bars corresponding to standard deviation are plotted, even if too small to be visible. $N$ is the number of monomers of the ring polymer and $R_g^0$ is the average radius of gyration of the passive ring polymer in unconfined space.

Figure 4

The effective translational diffusion coefficient ($D_T^{F_a}$) of the flexible and inextensible ring polymers ($N=50$) subjected to different activity in porous medium with $\xi =6.92$.

Figure 5

$P\left(R_g\right)\text{vs}{R}_g$ for flexible [(a), (d)], inextensible [(b), (e)], and semiflexible [(c), (f)] ring polymers ($N=50$) subjected to different activity in the unconfined space and porous medium with $\xi =6.92$, respectively.

Figure 6

$\langle C_{R_g}\left(\tau \right)\rangle \text{vs}\tau$ for flexible (a), inextensible (b), and semiflexible (c) ring polymers ($N=50$) subjected to different activity in the porous medium with $\xi =6.92$.

Figure 7

The COM trajectory, log-log plot of $\langle \overline{\mathrm{\Delta }{r}_c^2\left(\tau \right)}\rangle \text{vs}\tau$, log-linear plot of $\alpha \left(\tau \right)\text{vs}\tau$, and $P\left(R_g\right)\text{vs}{R}_g$ of the ring subjected to different $F_a$ for flexible ($N=100$) [(a), (b), (c), and (d)] and semiflexible ($N=50$) [(e), (f), (g), and (h)] ring polymers in the porous medium with $\xi =$ 6.92 and 9.84, respectively. For each time interval $\tau$, the error bars corresponding to standard deviation are plotted in $\langle \overline{\mathrm{\Delta }{r}_c^2\left(\tau \right)}\rangle$ [(b), (f)] and $\alpha \left(\tau \right)$ [(c), (g)], even if too small to be visible.