We study the shear induced migration of microswimmers (primarily, active Brownian particles or ABP's) in a plane Poiseuille flow. For wide channels characterized by $U_b/HD_r \ll 1$, the separation between time scales characterizing the swimmer orientation dynamics (of O($D^{-1}_r$)) and those that characterize migration across the channel (of O($H^{2}D_r/U^{2}_b$)), allows for use of the method of multiple scales to derive a drift-diffusion equation for the swimmer concentration profile; here, $U_b$ is the swimming speed, $H$ is the channel half-width, and $D_r$ is the swimmer rotary diffusivity. The steady state concentration profile is a function of the Peclet number, $Pe = U_{f}/(D_r H)$ ($U_f$ being the channel centerline velocity), and the swimmer aspect ratio $\kappa$. Swimmers with $ \kappa \gg 1$ (with $ \kappa \sim$ O(1)), in the regime $1 \ll \textit{Pe} \ll \kappa^3$ ($Pe\sim$ O(1)), migrate towards the channel walls, corresponding to a high-shear trapping behavior. For $Pe \gg \kappa^3 $ ($Pe \gg $ 1 for $\kappa \sim$ O(1)), however, swimmers migrate towards the centerline, corresponding to a low-shear trapping behavior. Interestingly, within the low-shear trapping regime, swimmers with $\kappa < 2$ asymptote to a $Pe$-independent concentration profile for large $Pe$, while those with $\kappa \geq 2$ exhibit a `centerline-collapse' for $Pe \to \infty$. The prediction of low-shear-trapping, validated by Langevin simulations, is the first explanation of recent experimental observations [Barry $\textit{et al}$. (2015)]. We organize the high-shear and low-shear trapping regimes on a $Pe-\kappa$ plane, thereby highlighting the singular behavior of infinite-aspect-ratio swimmers.

中文翻译：

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压力驱动通道流中微型游泳者的剪切诱导迁移

我们研究了平面 Poiseuille 流中微型游泳者（主要是活性布朗粒子或 ABP）的剪切诱导迁移。对于以 $U_b/HD_r \ll 1$ 为特征的宽通道，表征游泳者方向动力学的时间尺度（O($D^{-1}_r$)）和表征跨通道迁移的时间尺度之间的分离（O ($H^{2}D_r/U^{2}_b$))，允许使用多尺度方法来推导出游泳者浓度分布的漂移扩散方程；其中，$U_b$ 是游泳速度，$H$ 是通道半宽，$D_r$ 是游泳者旋转扩散率。稳态浓度分布是 Peclet 数的函数，$Pe = U_{f}/(D_r H)$（$U_f$ 是通道中心线速度）和游泳者纵横比 $\kappa$。游泳者 $ \kappa \gg 1$（$ \kappa \sim$ O(1)），在 $1 \ll \textit{Pe} \ll \kappa^3$ ($Pe\sim$ O(1)) 状态下，向通道壁迁移，对应于高剪切捕获行为。然而，对于 $Pe \gg \kappa^3 $（$Pe \gg $ 1 for $\kappa \sim$ O(1)），然而，游泳者向中心线迁移，对应于低剪切诱捕行为。有趣的是，在低剪切诱捕机制中，$\kappa < 2$ 的游泳者渐近到与 $Pe$ 无关的大 $Pe$ 浓度分布，而那些具有 $\kappa\geq 2$ 的游泳者表现出“中心线塌陷” ' 对于 $Pe \to \infty$。由朗之万模拟验证的低剪切俘获的预测是最近实验观察的第一个解释 [Barry $\textit{et al}$. (2015)]。我们在 $Pe-\kappa$ 平面上组织高剪切和低剪切捕获机制，