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arXiv 1809.02102physics.flu-dyncond-mat.soft
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稀释细菌悬液中的应力松弛：主动-被动转变

Stress relaxation in a dilute bacterial suspension: The active-passive transition

Sankalp Nambiar, Phanikanth S, Nott P. R., Ganesh Subramanian

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摘要：

我们分析了稀释的细菌悬浮液的时间依赖性非线性流变学（例如E。大肠杆菌）的一对冲动开始的线性流动-简单剪切和单轴拉伸。流变学由细菌取向分布决定，其满足动力学方程，该动力学方程包括由施加的流动引起的旋转，以及通过旋转扩散和翻滚而松弛至各向同性。相关的无量纲参数是Peclet数$Pe\equiv \dotγτ$和$τD_r$，Peclet数决定了流动诱导取向各向异性的重要性，$τD_r$量化了两种内在取向去相关机制（翻滚和旋转扩散）的相对重要性。这里，$τ$是表现出奔跑-翻滚动力学的细菌的平均奔跑持续时间，$D_r$是细菌的固有旋转扩散率，而$\dotγ$是施加的速度梯度的特征幅度。动力学方程的解决方案是使用频谱伽辽金法数值获得的，并在整个范围内的$Pe$产生相关的流变性能。对于简单剪切，我们在小$Pe$下的分析预测的应力松弛与Lopez等人（2015）的实验观察结果非常一致。然而，在大$Pe$上的分析产生了性质上不同的弛豫。实验中的流变学响应对应于从小$Pe$的主动游泳者的近各向同性悬浮到大$Pe$的被动杆的明显（近）各向同性悬浮的过渡。相比之下，计算产生了预期的过渡到一个几乎流动对齐悬浮被动刚性棒在高$Pe$。我们探测这种主动-被动过渡系统，补充数值解与解析解从适当的基态微扰展开。

英文摘要：

We analyse the time dependent non-linear rheology of a dilute bacterial suspension (e.g. E. coli) for a pair of impulsively started linear flows - simple shear and uniaxial extension. The rheology is governed by the bacterium orientation distribution which satisfies a kinetic equation that includes rotation by the imposed flow, and relaxation to isotropy via rotary diffusion and tumbling. The relevant dimensionless parameters are the Peclet number $Pe\equiv \dotγτ$, which dictates the importance of flow-induced orientation anisotropy, and $τD_r$, which quantifies the relative importance of the two intrinsic orientation decorrelation mechanisms (tumbling and rotary diffusion). Here, $τ$ is the mean run duration of a bacterium that exhibits a run-and-tumble dynamics, $D_r$ is the intrinsic rotary diffusivity of the bacterium and $\dotγ$ is the characteristic magnitude of the imposed velocity gradient. The solution of the kinetic equation is obtained numerically using a spectral Galerkin method, and yields the relevant rheological properties over the entire range of $Pe$. For simple shear, the stress relaxation predicted by our analysis at small $Pe$ is in good agreement with the experimental observations of Lopez et al. (2015). However, the analysis at large $Pe$ yields relaxations that are qualitatively different. The rheological response in the experiments corresponds to a transition from a nearly isotropic suspension of active swimmers at small $Pe$, to an apparently (nearly) isotropic suspension of passive rods at large $Pe$. In contrast, the computations yield the expected transition to a nearly flow-aligned suspension of passive rigid rods at high $Pe$. We probe this active-passive transition systematically, complementing the numerical solution with analytical solutions obtained from perturbation expansions about appropriate base states.

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