Inertial active particles in a Poiseuille flow: negative mobility and particle separation

TL;DR

This work analyzes how inertia affects the transport of inertial active Brownian particles in a 2D Poiseuille flow, aiming to enable mass-based particle separation. Using a Langevin framework with mass $m$, self-propulsion $f_0$, diffusion $(D_t,D_r)$, and external rotation $\Omega$, the authors simulate trajectories in a confined channel and quantify the mean drift $\langle v \rangle$ and effective diffusion $D_{eff}$. They find a nonmonotonic dependence of transport on mass, including negative mobility in the overdamped limit and an optimal mass $m_{op}$ that maximizes downstream drift and diffusion, along with inertia-induced wall accumulation at large $m$. The activity $f_0$ and rotation rate $\Omega$ further tune these effects, enabling selective, mass-based transport in microfluidic environments. These results establish inertia as a practical control parameter for passive separation strategies and suggest extensions to 3D geometries and hydrodynamic interactions for lab-on-chip applications.

Abstract

The diffusive behavior of small entities is strongly influenced by the flow of the surrounding medium, which is ubiquitous in natural and artificial environments. In this study, we investigate the transport characteristics of the inertial active Brownian particles (ABPs) in a microfluidic channel under a Poiseuille flow. The interplay between the inertia of the particles and the imposed fluid flow leads to interesting diffusive behaviors. For instance, in the overdamped regime ($m \to 0$), particles exhibit a negative average velocity $\langle v \rangle$ due to upstream movement. As $m$ increases, particles tend to move along the flow direction with an increase in $\langle v \rangle$ in the positive direction, exhibiting a maximum at optimal $m$, and diminish for higher $m$ values. The effective diffusion coefficient $D_{eff}$ also shows a peak at this optimal $m$. Interestingly, at higher $m$ values, $D_{eff}$ decreases with increasing the noise strength. The self-propelled velocity of the particles further enhances the upstream movement. Further, the rotation rate of the particles also contributes positively to the upstream motion, and enhances the diffusion of the particles by many orders in the limit of higher $m$. This study reveals that inertia not only modifies swimmer flow interactions but also enables new dynamical regimes, where mass-dependent trajectories can be harnessed for selective control. Such control holds promise for mass based particle separation in precisely engineered environments and lab on a chip devices for technological applications.

Figures (7)

• Figure 1: Schematic of an ABP in a 2D microfluidic channel under a Poiseuille flow $u(y)$. The particle is located at $r = (x, y)$ and has a constant intrinsic speed in the direction of its orientation $\hat{n}$. The active force $F_0$, self-propelled angle $\theta$, chirality $\Omega$, local shear rate $\omega(y)$, and width of the channel $y_L$ are indicated.
• Figure 2: (a)-(c) Deterministic trajectories of an active particle in a two-dimensional channel with a Poiseuille flow prescribed by Eq. \ref{['poe_eq']}. The particle starts at the center of the channel, i.e., $x = y = 0$, with different values of particle mass. (d)-(f) are the corresponding orientation $\theta$(t) and the instantaneous velocity $\phi_v$(t) directions. For $m\neq 0$, a lag develops between $\theta$(t) and $\phi_v$(t) due to the inertia of the particles. Trajectories are obtained by integrating Eq. \ref{['eq:Lan-dl']} and Eq. \ref{['eq:Lan-dlth']} numerically for $D_t = D_r = 0$, $\Omega = 0$, and $f_0 = 1$.
• Figure 3: (a) The average velocity $\langle v \rangle$ and (b) the effective diffusion coefficient $D_{eff}$ as a function mass $m$ of the particles for various values of the diffusion coefficient $D=D_r=D_t$. The horizontal dashed line indicates the maximum flow velocity in the channel, $\langle v_x \rangle_{limit}$ (Eq. \ref{['eq:vx']}). The other parameters are set as, $\Omega = 0$ and $f_0 = 1$.
• Figure 4: The steady state distribution of chiral particles, for various values of the diffusion coefficient $D$. The other parameters are set as, $m=100$, $u_0=1$, $\Omega = 0$ and $f_0 = 1$.
• Figure 5: (a) The average velocity $\langle v \rangle$ and (b) the effective diffusion coefficient $D_{eff}$ as a function mass $m$ for various values of the rotational diffusion coefficient $D_r$ with $D_t=0.01$. (c) The average velocity $\langle v \rangle$ and (d) the effective diffusion coefficient $D_{eff}$ as a function of mass $m$ for various values of the translational diffusion coefficient $D_t$ with $D_r=0.01$. The other parameters are set as, $\Omega = 0$ and $f_0 = 1$.