Anomalous dynamics of an elastic membrane in an active fluid

Using numerical simulations, we characterized the behavior of an elastic membrane immersed in an active fluid. Our findings reveal a nontrivial folding and re-expansion of the membrane that is controlled by the interplay of its resistance to bending and the self-propulsion strength of the active components in solution. We show how flexible membranes tend to collapse into multifolded states, whereas stiff membranes fluctuate between an extended configuration and a singly folded state. This study provides a simple example of how to exploit the random motion of active particles to perform mechanical work at the microscale.

Figure 1

Reference snapshots showing the various conformations taken by the membrane as the bath activity and bending rigidity is varied. (a) flat/extended, (b) bent, (c) single folded, and (d) multifolded.

Figure 2

The time average of the radius of gyration $\langle R_g\rangle$ (left) and asphericity $\langle A\rangle$ (right) as a function of $\text{Pe}$ for membranes of different bending rigidities ${\kappa }_b$.

Figure 3

Probability distribution of the radius of gyration $P\left(R_g\right)$ for membranes of increasingly large Peclet numbers. Different panels show the results for different bending rigidities of the membrane as indicated. The letters in parentheses indicate the corresponding configurations as shown in Fig. 1.

Figure 4

Probability distribution of the asphericity $P\left(A\right)$ for membranes of increasingly large Peclet numbers. Different panels refer to different bending rigidities of the membrane as indicated. The letters in parentheses indicate the corresponding configurations as shown in Fig. 1.

Figure 5

Joint probability distribution of the membrane shape $P(A,R_g)$ for a fixed Peclet number $\text{Pe}=50$ and various bending rigidities.