论文标题
微观群体的异常分散
Anomalous dispersion of microswimmer populations
论文作者
论文摘要
我们检查了压力驱动通道流动中球体微晶状体的纵向分散。当时间尺度对应于游泳者方向放松以及在梯度和流动方向的扩散良好时，多个尺度分析会导致剪切增强的扩散率，控制游泳器沿流量沿流动\（纵向）方向的长期扩散。对于大的$ pe_r $，$ pe_r $是旋转的peclet编号，这种扩散率缩放为$ o（pe_r^4d_t）$，$ 1 \ leqκ\ lyssim 2 $ 2 $ 2 $，as $ o（pe_r^{\ frac {\ frac {10}}} {3}} {3}} d_t d_t d_t d_t）转化扩散率和$κ$游泳者长宽比。对于$ 2 \Lesssimκ<\ infty $，游泳者以增加$ pe_r $倒在中心线上，导致异常降低$ O（pe_r^{5+c（κ）} d_t）$的扩散率。在这里，$ c（κ）\！<\！ - 1 $表征了$ O（pe_r^{ - 1}）$ central核心在$ O（pe_r^{ - 1}）之外的代数衰减，其异常指数由大型速度变化控制，由该核心以外的少数游泳者采样。 $ c（κ）$下降到低于$ -5 $的$κ\ gtrsim 10 $，导致$ O（κ^{10} d_t）$的流动独立界限，用于分散足够细长的游泳者。
We examine the longitudinal dispersion of spheroidal microswimmers in pressure-driven channel flow. When time scales corresponding to swimmer orientation relaxation, and diffusion in the gradient and flow directions, are well separated, a multiple scales analysis leads to the shear-enhanced diffusivity governing the long-time spread of the swimmer population along the flow\,(longitudinal) direction. For large $Pe_r$, $Pe_r$ being the rotary Peclet number, this diffusivity scales as $O(Pe_r^4D_t)$ for $1 \leq κ\lesssim 2$, and as $O(Pe_r^{\frac{10}{3}}D_t)$ for $κ= \infty$, $D_t$ being the (bare)\,swimmer translational diffusivity and $κ$ the swimmer aspect ratio. For $2 \lesssim κ< \infty$, swimmers collapse onto the centerline with increasing $Pe_r$, leading to an anomalously reduced diffusivity of $O(Pe_r^{5+C(κ)}D_t)$. Here, $C(κ)\!<\!-1$ characterizes the algebraic decay of swimmer concentration outside an $O(Pe_r^{-1})$ central core, with the anomalous exponent governed by large velocity variations sampled by the few swimmers outside this core. $C(κ)$ dips below $-5$ for $κ\gtrsim 10$, leading to a flow-independent bound of $O(κ^{10}D_t)$ for the dispersion of sufficiently slender swimmers.
