Separation of interacting active particles in an asymmetric channel

We study the diffusive behavior of interacting active particles (self-propelled) with mass $m$ in an asymmetric channel. The particles are subjected to an external oscillatory force along the length of the channel. In this setup, particles may exhibit rectification. In the absence of interaction, the mean velocity $\langle v\rangle$ of the particles shows a maximum at moderate $m$ values. It means that particles of moderate $m$ have higher velocities than the others. However, by incorporating short-range interaction between the particles, $\langle v\rangle$ exhibits an additional peak at lower $m$ values, indicating that particles of lower and moderate $m$ can be separated simultaneously from the rest. Furthermore, by tuning the interaction strength, the self-propelled velocity, and the parameters of the oscillatory force, one can selectively separate the particles of lower $m$, moderate $m$, or both. Empirical relations for estimating the optimal mass as a function of these parameters are proposed. These findings are beneficial for separating the particles of selective $m$ from the rest of the particles.

Figure 1

Schematic illustration of a 2D asymmetric channel, described by Eq. (3), with the periodicity $L$ confining the motion of an active Brownian particle of mass $M$. The particle propels with a self-propelled velocity $v_0=F_0/\eta$ and is subjected to oscillatory force $F\left(t\right)$. Equation (5) describes the interaction between the particles.

Figure 2

(a) The mean velocity $\langle v\rangle$ and (b) the effective diffusion coefficient $D_{\mathrm{eff}}$ as a function of the mass $m$ of the active particles for different strengths of the interaction $k$ between the particles. The amplitude $a$ and the frequency $\omega$ of the oscillatory force are set to $\omega =0.1$ and $a=2.5$. The geometry of the channel is described by Eq. (3) with the channel aspect ratio $\epsilon =0.1$.

Figure 3

$\langle v\rangle L/D_{\mathrm{eff}}$ as a function of the mass $m$ of the active particles for different strengths of the interaction $k$ between the particles. The amplitude $a$ and the frequency $\omega$ of the oscillatory force are set to $\omega =0.1$ and $a=2.5$, with the channel aspect ratio $\epsilon =0.1$ and $L=1$.

Figure 4

The mean velocity $\langle v\rangle$ as a function of the mass $m$ of the interacting particles for different strengths of frequency $\omega$ (a) and amplitude $a$ (b) of the oscillatory force. The geometry of the channel is described by Eq. (3) with the channel aspect ratio $\epsilon =0.1$. Here, the particle interaction strength $k=350$.

Figure 5

The average velocity $\langle v\rangle$ as a function of the mass $m$ of active particles for different values of channel aspect ratio $\epsilon$. The geometry of the channel is described by Eq. (3). The amplitude $a$ and the frequency $\omega$ of the oscillatory force are set to $\omega =0.1$ and $a=2.5$. Here, the particle interaction strength $k=350$.

Figure 6

The average velocity as a function of the mass of active particles for different strengths of the self-propelled velocity $v_0$. The particle interaction strength $k=350$. The geometry of the channel is described by Eq. (3) with an aspect ratio $\epsilon =0.1$.