The stability of a homogeneous suspension of chemotactic bacteria
The stability of a homogeneous suspension of chemotactic bacteria
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DOI：
10.1063/1.3580271
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发表时间：
2011-04-01
影响因子：
4.6
通讯作者：
Fitzgibbon, Sean R.
中科院分区：
文献类型：
--
作者：
Subramanian, G.;Koch, Donald L.;Fitzgibbon, Sean R.
分析了趋化细菌均一稀悬浮液在恒定吸引剂梯度下的线性稳定性。细菌进行一种奔跑和翻滚的运动，以大肠杆菌为代表，其中平稳的游泳(奔跑)时期被游泳方向的突然不相关变化(翻滚)打断。当细菌游向化学吸引剂浓度较高的区域时，细菌翻滚的频率较低，从而导致细菌在碱性状态下的平均取向和速度。无界悬浮液的稳定性，无论有没有化学吸引剂，都是由流体速度场和细菌定向场的耦合长波扰动控制的。在前一种情况下，最不稳定的微扰使其波矢沿化学吸引剂的梯度定向。与Subramanian和Koch的预测相比，趋化性降低了集体游泳开始的临界细菌浓度[“集体游泳开始的关键细菌浓度”，J.632,359(2009)]在没有化学引诱剂的情况下。这种减少的一部分可以归因于在存在化学吸引剂梯度的情况下平均翻滚时间的增加。第二个不稳定的影响来自剪切运动的能力，与速度扰动相关，其中速度和化学梯度对齐，将预先排列的细菌扫入局部伸展象限，从而产生比最初各向同性悬浮液中更强的不稳定主动应力。化学吸引剂的梯度也从根本上改变了任何有限波数的不稳定谱。在不翻滚的细菌悬浮液中，Saintillan和Shelley[《活性粒子悬浮液中的不稳定性和图案形成：动力学理论和连续介质模拟》，物理。莱特牧师。178103(2008年)；《活性悬浮液中的不稳定性、模式形成和混合》，Phys。流体20,123304(2008年)]表明，增长率在临界波数以下有两个实解(驻留模)，在临界波数下，这两个解合并，然后分叉，形成一对较大波数的复共轭解(传播模)。离散谱终止于第二个临界波数，在这个波数之外，唯一剩下的解是组成连续谱的中性稳定波。然而，在化学吸引剂梯度的存在下，上述完美分叉被打破，并且找到了所有波数的一对行波解。此外，增长率的解不是终止于临界波数，而是在大波数时渐近于滚落频率的负值。(C)2011年美国物理研究所。[DOI：10.1063/1.3580271]
The linear stability of a homogeneous dilute suspension of chemotactic bacteria in a constant chemoattractant gradient is analyzed. The bacteria execute a run-and-tumble motion, typified by the species E. coli, wherein periods of smooth swimming (runs) are interrupted by abrupt uncorrelated changes in swimming direction (tumbles). Bacteria tumble less frequently when swimming toward regions of higher chemoattractant concentration, leading to a mean bacterial orientation and velocity in the base state. The stability of an unbounded suspension, both with and without a chemoattractant, is controlled by coupled long wavelength perturbations of the fluid velocity and bacterial orientation fields. In the former case, the most unstable perturbations have their wave vector oriented along the chemoattractant gradient. Chemotaxis reduces the critical bacteria concentration, for the onset of collective swimming, compared with that predicted by Subramanian and Koch ["Critical bacterial concentration for the onset of collective swimming," J. Fluid Mech. 632, 359 (2009)] in the absence of a chemoattractant. A part of this decrease may be attributed to the increase in the mean tumbling time in the presence of a chemoattractant gradient. A second destabilizing influence comes from the ability of the shearing motion, associated with a velocity perturbation in which the velocity and chemical gradients are aligned, to sweep prealigned bacteria into the local extensional quadrant thereby creating a stronger destabilizing active stress than in an initially isotropic suspension. The chemoattractant gradient also fundamentally alters the unstable spectrum for any finite wavenumber. In suspensions of bacteria that do not tumble, Saintillan and Shelley ["Instabilities and pattern formation in active particle suspensions: Kinetic theory and continuum simulations," Phys. Rev. Lett. 100, 178103 (2008); " Instabilities, pattern formation and mixing in active suspensions," Phys. Fluids 20, 123304 (2008)] showed that the growth rate has two real solutions (stationary modes) below a critical wavenumber at which the two solutions merge and then bifurcate to form a pair of complex conjugate solutions (propagating modes) for larger wavenumbers. The discrete spectrum terminates at a second critical wavenumber, and beyond this wavenumber, the only remaining solutions are neutrally stable waves comprising the continuous spectrum. In the presence of a chemoattractant gradient, however, the aforementioned perfect bifurcation is broken and a pair of traveling wave solutions is found for all wavenumbers. Furthermore, instead of terminating at a critical wavenumber, the solutions for the growth rate asymptote to the negative of the tumbling frequency at large wavenumbers. (C) 2011 American Institute of Physics. [doi:10.1063/1.3580271]