Sorting of binary active-passive mixtures in designed microchannels

TL;DR

The study demonstrates that sorting passive particles in active–passive mixtures can be optimized by designing funnel-like microchannels and tuning the active bath's persistence via the tumbling rate. Through 2D simulations, passive transport and separation are maximized at intermediate $\\alpha$ and large funnel angles, with a peak bottom enrichment around $\\langle \\mathcal{F}_{bottom}\\rangle \\approx 0.92$ for $\\theta_{obs}=75^{\\circ}$. A minimal one-dimensional Advection–Diffusion model shows that negative active drift in the top region, rather than diffusivity contrast alone, drives the sorting, capturing the essential physics with a simple framework. The findings reveal an active-pumping mechanism, suggesting practical routes for microfluidic cargo sorting and bioremediation, and point to future work incorporating hydrodynamics and experimental realizations with microalgae-bead mixtures.

Abstract

Mixtures of active and passive particles are ubiquitous at the microscale. Many essential microbial processes involve interactions with dead or immotile cells or passive crowders. When passive objects are immersed in active baths, their transport properties are enhanced and can be tuned by controlling active agents' spatial and orientational distribution. Active-passive mixtures provide a platform to explore fundamental questions about the emergent behaviour of passive objects under simultaneous thermal and active noise and a foundation for technological applications in cargo delivery and bioremediation. In this work, we use computational simulations to study an active-passive mixture confined in microchannels designed with funnel-like obstacles that selectively allow the passage of passive particles. Active particles follow overdamped Langevin translational dynamics and run-and-tumble rotational dynamics. We find that adjusting the tumbling rate of active agents and the microchannel geometry leads to a maximum enhancement of the transport properties of the passive particles (diffusion coefficient and advective velocity) that correlates with the highest mixture sorting efficiency and the shortest response time.

Figures (7)

• Figure 1: The system and geometry of the microchannel. Pink particles are active, and their orientation vector is represented in dark red. Blue particles are passive, and yellow particles are frozen and constituents of the channel's walls. The funnel-like obstacles in the central region of the channel have gaps that only allow the passage of passive particles. The active-passive binary mixture is confined in the $y$-axis by placing walls at $y = l_w$ and $y = L_y - l_w$. Periodic boundary conditions are applied along the $x$-axis. (a) The particles are initially placed in random positions in the top compartment. (b) At the steady state, the sorting of the mixture is achieved; the concentration of passive particles in the bottom compartment is much higher than that of the top compartment.(c) The gap between obstacles is $\Delta = 1.25\sigma_{22}$ and the angle between the obstacles and the $x$-axis is $\theta_{obs}$. The length of the obstacles is $\mathcal{L} = 3\sigma_{11}$. The reference for the concave and convex regions is the top compartment of the microchannel. The blue dashed-line rectangles represent the funnels composed of two barriers labeled as "left" and "right". For the concave gaps, the clogging region for $\theta_{obs}\leq30^{\circ}$ is that consisting of the intersection of the yellow semi-circles of radius, $R = \sigma_{33}/2 +\sigma_{22} + \sigma_{11}/2$, in the funnel $k$, and for $\theta_{obs}>30^{\circ}$ the clogging area is that consisting of the area below the straight lines parallel to the barriers at a distance $R$ from the center of the barrier and depicted in dark orange in funnel $k$. For the convex gaps, the clogging region is defined as the intersection of 2 circles placed at the center of the extreme wall particles with radius, $R$. All the graphics of trajectories of simulations presented in this article were generated in part using the visualization software Ovito stukowski2009visualization.
• Figure 2: The sorting process follows first-order dynamics. The simulation data is represented with circles, and the fits to the first-order dynamics are expressed in equation \ref{['e:sol_N_bottom']} in solid lines. The curves are represented in a semi-log scale in the $x$ axis and have a positive shift of $0.20$ in the $y$-axis for clarity. (a) The fraction of passive particles in the bottom compartment, $\mathcal{F}_{bottom}$ as a function of time. The active particles' tumbling rate, $\alpha = 1\times10^{-4}$, is kept constant, whereas the angle of the obstacles $\theta_{obs}$ is varied. (b)$\mathcal{F}_{bottom}$ as a function of time when the angle of the obstacles, $\theta_{obs} = 45^{\circ}$ and $\alpha$ is changing.
• Figure 3: The dependence of the dynamic parameters on the activity and geometry.(a) the average fraction of passive particles in the bottom compartment at steady state, $\langle \mathcal{F}_{bottom} \rangle$ and (b) the time constant of the sorting process as functions of the tumbling rate of the active particles, $\alpha$, and the angle of the obstacles $\theta_{obs}$. In (a) solid lines are predictions of the model in eq. \ref{['e:ODE_first_order']} given by $\mathcal{F}_{bottom}= \frac{k^+\mathcal{F}_{top}}{k^-}$ and in (b) are guides for the eye. The inset in (a) is $\langle\mathcal{F}_{bottom}\rangle$ as a function of the persistence length, $l_p = \frac{F_a dt}{\alpha\gamma_1}$. The inset in (b) is $f(\theta_{obs},\alpha)$ as presented in \ref{['eq:taud']} . Figure (a) is presented in a semi-log scale in the $x$-axis and figure (b) in a log-log scale.
• Figure 4: Dependence of the available cavities for the passive particles to flow on the activity and geometry.(a) The fraction of open concave cavities, $\mathcal{P}_{concave}$. The inset contains the clogging area, $A_c$, as a function of $\theta_{obs}$. Details on how to estimate the clogging area can be found in Fig.S2(b) The fraction of open convex cavities $\mathcal{P}_{convex}$, and (c) the total fraction of open cavities, $\mathcal{P}_{total}$ as functions of the tumbling rate, $\alpha$ and the angle of the obstacles, $\theta_{obs}$
• Figure 5: Drift velocity in the $y$-direction induced by the concomitant effect of activity and confinement The drift velocity in the top compartment of the microchannel as a function of the tumbling rate, $\alpha$, and the angle of the obstacles, $\theta_{obs}$.