Diffusion of gravitactic chiral active Brownian particles in an asymmetric channel

Abstract

The diffusion of micro- and nanoswimmers in a fluid, confined within irregular structures that impose entropic barriers, is often modeled using overdamped active Brownian dynamics, where viscous effects are paramount and inertia is negligible. Here, we numerically investigate the diffusive behavior of chiral self-propelled particles in a two-dimensional asymmetric channel subjected to an external torque arising from a gravitational field. We reveal the emergence of resonant diffusion when the external torque $ω$ approaches the intrinsic angular velocity $ω_{0}$ of particles. This resonance manifests as a pronounced accumulation of particles near the upper-left corner of the channel, accompanied by an enhanced peak in the effective diffusion coefficient. In particular, it is observed only for low rotational diffusion rates and does not persist beyond moderate values of $ω_{0}$. Prominent transport features, such as rectification at low values of $ω$, a monotonic increase in average velocity with $ω$, and a nonmonotonic response of transport characteristics (average velocity and effective diffusion coefficient) as a function of the rotational diffusion rate near the resonance point, are explained. Furthermore, we show that the transport characteristics depend strongly on the aspect ratio of the channel. For instance, the enhanced diffusion peak becomes more pronounced with increasing aspect ratio, and the average velocity saturates at higher values for wider bottleneck openings. It is conceivable that these findings have a great potential for developing microfluidic and laboratory-on-a-chip devices for particle separation, targeted drug delivery, and advanced active materials.

Figures (7)

• Figure 1: Schematic illustration of an active (self-propelled) Brownian particle diffusing in a two-dimensional triangular channel with periodicity $L$. The self-propelled velocity $V_0 \boldsymbol{\hat{n}}$, angle $\theta$, intrinsic angular velocity $\Omega_{0}$, gravitational force $\boldsymbol{F} = F \boldsymbol{\hat{y}}$, gravitational torque $\Omega \sin \theta$, local width of the channel $2~\mathrm{w}(x)$, and local length of a cell of the channel $\Delta (y)$ are indicated. The particle is restricted from penetrating the rigid channel walls; however, it remains free to rotate and slide along the walls.
• Figure 2: (a)-(c) Steady-state distribution of particles, mapped onto a single cell of the channel, for different values of torque $\omega$. (d) Corresponding probability densities $P_{st} (y)$ along the $y$ direction. The parameters are $v_{0} = 10, \omega_{0} = 0.01, \alpha = 0.01$, and $\epsilon = 0.1$.
• Figure 3: (a)-(c) Steady-state distribution of particles for different values of the scaled rotational diffusion rate $\alpha$ at $\omega/\omega_{0} = 1$. (d) Corresponding probability densities $P_{st} (y)$ versus $y$. The parameters are $v_{0} = 10, \omega_{0} = 0.01, \omega = 0.01$, and $\epsilon = 0.1$.
• Figure 4: Average velocity $v$ as a function of the torque $\omega$ is shown in (a) for different values of the intrinsic angular velocity $\omega_{0}$. The corresponding effective diffusion coefficient $D_{\mathrm{eff}}$ is shown in (b). The insets plot $v$ and $D_{\mathrm{eff}}$ versus $\omega$ on an expanded scale for selected values of $\omega_0$. Here and below, solid lines serve as guides to the eye. The other parameters are $v_{0} = 1, \alpha = 0.01$, and $\epsilon = 0.1$.
• Figure 5: Average velocity $v$ and effective diffusion coefficient $D_{\mathrm{eff}}$ as a function of torque $\omega$ are shown in (a) and (b), respectively, for different values of the rotational diffusion rate $\alpha$. The inset plots $D_{\mathrm{eff}}$ versus $\omega$ for $\alpha = 0.1$, $\alpha = 1$, and $\alpha = 10$ on an expanded scale. The other parameters are $v_{0} = 1, \omega_{0} = 0.01$, and $\epsilon = 0.1$.