Field-Particle Interactions in Curved Flows for Shape-Asymmetric Active Particles

Abstract

We show that curvatures in general ambient flow profiles can align shape-asymmetric active particles, revealing a previously overlooked competition with externally applied aligning fields. Focusing on the ubiquitous case of channel flows, we then investigate the fundamental consequences of this competition for the dynamics of shape-asymmetric active particles in microchannels in the presence of orienting fields. We find that this interplay gives rise to novel mechanisms for controlling particle dynamics, with potentially broad applications, and suggests exciting possibilities such as active-particle analogs of electronic systems.

Figures (3)

• Figure 1: Polar alignments from flow and fields: (a) Flow ${\bf u}({\bf r})$ expanded about the hydrodynamic center ${\bf r}_h$ of an HT-A swimmer oriented along $\hat{\bf n}$. Leading-order rotational and straining flows [$(i)$] generate Jeffery-type, $\hat{\bf n} \to -\hat{\bf n}$ symmetric rotations, whereas second-order gradients [$(ii)$] break this symmetry. (b) Steady orientations arise from four contributions: flow vorticity (maroon), polar alignment to the field ${\bf E}_f$ (orange), flow-induced polar alignment $\propto\beta_1,\beta_3$ along/against the local flow (blue), and apolar alignment $\propto\beta_2$ along the straining axis [cf. $(a)-(i)$]. (c) Contribution to $\dot\theta \equiv \omega_z$ from the flow (blue) and the field (yellow) plotted function of $\theta$ for Poiseuille flow at $y=0, \theta_0=\pi$ and $\overline{E}=0.2$. Inset: zoom near $\theta=\pi$.
• Figure 2: (a) HT-S dynamics: Trajectories for different initial heights $y_i$ at $\theta_i=\pi$ with a field at $\theta_0=3\pi/4$. Inset: Same $y_i,\theta_i$ for $\theta_0=\pi/4$. (b) Schematic of HT-S/HT-A particles with two symmetric field sources on (top) and with only one source on (bottom). (c) HT-A dynamics: (Left panel) Trajectories for two different field strengths $\overline{E}_1,\overline{E}_2$, with three $y_i$ common to both $\overline{E}$, (Right panel) Trajectories for $\overline{E}_3,\overline{E}_4$, with a another set of three common $y_i$. $\overline{E}_1>\cdots>\overline{E}_4$. All have $\theta_i=\pi$. (d) Phase space at $\theta_0=3\pi/4$ ($\overline{E}=0.35$), showing the stable fixed point (s-FP, green), unstable limit cycle (u-LC, dashed red), stable limit cycle (s-LC, filled red), and separatrix (blue). (e) Corresponding $y_{\pi}$ values of the s-FP, u-LC, s-LC, and separatrix vs. $\overline{E}$, at $\theta=\pi$ , with arrows indicating effective trajectory directions. (f) Phase space at $\theta_0=\pi/4$ ($\overline{E}=0.35$), showing the unstable fixed point (u-FP) and separatrix (blue). Initial conditions starting at blue regions end up at the top wall; orange regions to the bottom. $\{a,b\}$ are the starting and $\{d,c\}$ are the ending points of the {lower,upper} separatrix. (g) Corresponding $y_{\pi}$ vs. $\overline{E}$ plot at $\theta_0=\pi/4$.
• Figure 3: Implications for swimmer populations. (a) HT-S particle currents $\bar{J}_{\rm H}$ (blue dot) and $\bar{J}_{\rm DC}$ (green dot) vs. $\overline{E}$ for $\theta_0=3\pi/4$; background color reflects the dominant current. Inset: corresponding currents for $\theta_0=\pi/4$. (b) HT-A currents for $\theta_0=3\pi/4$, showing the emergence of $\bar{J}_{\rm AC}$ (red) in regime $(ii)$ between regimes dominated by $\bar{J}_{\rm H}$ (blue)[$(ii)$] and $\bar{J}_{\rm DC}$ (green)[$(ii)$]. (c) Schematic HT-S concentration profiles and orientations for different field incidence angles $\theta_0$ across the $(x_0,y_0)$ quadrants; arrow colors encode deviation of orientation from upstream ($\theta=\pi$). (d) Top: Schematic HT-A population states for $\theta_0=3\pi/4$, corresponding to regimes $(i)-(iii)$ in panel b. Middle: Theoretically obtained $\dot{\psi}_a-\psi_a$ curves, indicating stability directions (colored arrows). The region beyond the separatrix is shaded gray with black arrows showing its instability. Bottom:$\dot{\psi}_a-\psi_a$ curves showing (left) the merger of separatrix and stable limit cycle (brown filled dot+gray region), and (right) the formation of a half-stable limit cycle (orange half-filled circle).