发表机构
Purdue University（普渡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过朗之万模拟和福克-普朗克模型，揭示振荡流通过沃默斯利数和频率比调控微游泳者横向输运，并建立普适传递定律预测贫化指数。
AI 中文摘要
能动微生物栖息于生理和工程系统中遇到的振荡流中，然而流动非定常性对其剪切诱导的优先聚集的影响仍知之甚少。我们利用互补的朗之万模拟以及二维和一维福克-普朗克模型，研究了细长微游泳者在振荡压力驱动通道流中的横向输运。在控制参数范围内，基于粒子和连续描述之间的一致性确立了福克-普朗克公式在振荡剪切流中游泳者输运的保真度。我们的分析表明，振荡强迫从根本上改变了经典的稳态流动剪切捕获。我们发现，增加沃默斯利数 $Wo$ 通过将振荡剪切限制在更薄的近壁区域来减少中心线贫化。相反，增加游泳者旋转扩散速率与流动振荡频率之比 $\beta$，促进持续的取向各向异性，并导致中心线贫化的饱和性增加。在弱游泳极限下，我们推导出一组耦合的取向矩的层级结构，使得在任意时间谐波阶数下都能获得解析解。渐近解建立了一个普适传递定律，表明对于给定的游泳者形状，归一化的前导阶取向响应仅取决于 $\beta$。取向分布的重建产生了游泳者浓度分布和贫化指数 $I_D$ 的闭式表达式。我们的渐近解恢复了稳态流动弱剪切下 $I_D$ 随流动佩克莱数 $Pe_f$ 的标度 $I_D \propto Pe_f^2$，并揭示振荡强迫通过因子 $16\beta^2/(1+16\beta^2)$ 衰减该响应。这些结果为预测微游泳者在振荡通道流中的横向输运提供了理论框架。
英文摘要
Motile microorganisms inhabit oscillatory flows encountered in physiological and engineering systems, yet the influence of flow unsteadiness on their shear-induced preferential concentration remains less understood. We investigate transverse transport of elongated microswimmers in oscillatory pressure-driven channel flow using complementary Langevin simulations and two- and one-dimensional Fokker-Planck models. Agreement between particle-based and continuum descriptions across governing parameters establishes the fidelity of the Fokker-Planck formulation for swimmer transport in oscillatory shear flows. Our analysis demonstrates that oscillatory forcing fundamentally modifies classical steady-flow shear-trapping. We find that increasing Womersley number $Wo$ reduces centerline depletion by confining oscillatory shear to thinner near-wall regions. In contrast, increasing frequency ratio $β$, of swimmer rotational diffusion rate and flow oscillation frequency, promotes sustained orientational anisotropy, and leads to a saturating increase in centerline depletion. In the weak-swimming limit, we derive a hierarchy of coupled orientational moments, enabling analytical solutions at arbitrary temporal harmonic order. The asymptotic solutions establish a universal transfer law showing that, for a given swimmer shape, the normalized leading-order orientational response depends solely on $β$. Reconstruction of the orientational distribution yields closed-form expressions for the swimmer concentration profile and depletion index, $I_D$. Our asymptotic solution recovers the steady-flow weak-shear scaling of $I_D$ with flow Peclet number, $Pe_f$, of $I_D \propto Pe_f^2$, and reveals that oscillatory forcing attenuates this response by a factor $16β^2/(1+16β^2)$. These results provide a theoretical framework to predict transverse transport of microswimmers in oscillatory channel flows.
