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

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.