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arXiv 1406.4264physics.flu-dyncond-mat.softphysics.bio-ph
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线性水流中主动游泳运动员的随机动力学

Stochastic dynamics of active swimmers in linear flows

Mario Sandoval, Navaneeth K. M., Ganesh Subramanian, Eric Lauga

摘要:

关于低雷诺数游泳的流体动力学的大多数经典工作都涉及静止环境中的确定性运动。已知流体中的热波动会导致游动方向的布朗损失。由于大多数细胞或合成的游泳者沉浸在外部流中,本文从理论上考虑了模型活性粒子(自推进球)在稳定的一般线性流中的随机动力学。随机性既来自物理空间中的平移扩散,也来自方向空间中的旋转扩散和翻滚动力学的组合。我们首先推导出一个一般配方的所有组件的长时间的均方位移张量的游泳者与时间相关的游泳速度,其方向decorrelates由于单独的旋转扩散。这个一般的框架是适用于获得对流增强均方位移的一个swelly-swimming粒子在三个典型的线性流(延伸,简单剪切,和固体旋转)。然后,我们将展示如何扩展我们的结果的情况下,游泳者的取向也decorrelates的运行和翻滚动力学帐户。自推进一般会导致相同的长时间的时间的线性流中的被动粒子的时间标度,但增加了系数。在特定的情况下,固体旋转,有效的长时间扩散是相同的,在一个静止的流体,我们澄清缺乏流动依赖性,通过简要检查椭圆线性流动的动态。通过比较新的主动条款与被动粒子,我们看到,游泳可以导致增强的均方位移的数量级,并可能是相关的生物有机体或合成的游泳设备在波动的环境或生物流。

英文摘要:

Most classical work on the hydrodynamics of low-Reynolds-number swimming addresses deterministic locomotion in quiescent environments. Thermal fluctuations in fluids are known to lead to a Brownian loss of the swimming direction. As most cells or synthetic swimmers are immersed in external flows, we consider theoretically in this paper the stochastic dynamics of a model active particle (a self-propelled sphere) in a steady general linear flow. The stochasticity arises both from translational diffusion in physical space, and from a combination of rotary diffusion and run-and-tumble dynamics in orientation space. We begin by deriving a general formulation for all components of the long-time mean square displacement tensor for a swimmer with a time-dependent swimming velocity and whose orientation decorrelates due to rotary diffusion alone. This general framework is applied to obtain the convectively enhanced mean-squared displacements of a steadily-swimming particle in three canonical linear flows (extension, simple shear, and solid-body rotation). We then show how to extend our results to the case where the swimmer orientation also decorrelates on account of run-and-tumble dynamics. Self-propulsion in general leads to the same long-time temporal scalings as for passive particles in linear flows but with increased coefficients. In the particular case of solid-body rotation, the effective long-time diffusion is the same as that in a quiescent fluid, and we clarify the lack of flow-dependence by briefly examining the dynamics in elliptic linear flows. By comparing the new active terms with those obtained for passive particles we see that swimming can lead to an enhancement of the mean-square displacements by orders of magnitude, and could be relevant for biological organisms or synthetic swimming devices in fluctuating environmental or biological flows.

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