We show that an inclusion placed inside a dilute Stokesian suspension of microswimmers induces power-law number-density modulations and flows. These take a different form depending on whether the inclusion is held fixed by an external force—for example, an optical tweezer—or if it is free. When the inclusion is held in place, the far-field fluid flow is a Stokeslet, while the microswimmer density decays as 1/𝑟2+𝜀, with 𝑟 the distance from the inclusion and 𝜀 an anomalous exponent which depends on the symmetry of the inclusion and varies continuously as a function of a dimensionless number characterizing the relative amplitudes of the convective and diffusive effects. The angular dependence takes a nontrivial form which depends on the same dimensionless number. When the inclusion is free to move, the far-field fluid flow is a stresslet, and the microswimmer density decays as 1/𝑟2 with a simple angular dependence. These long-range modulations mediate long-range interactions between inclusions that we characterize.

中文翻译：

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动量守恒活性流体中夹杂物的异常远程影响


我们表明，放置在微游泳者的稀 Stokesian 悬浮液中的夹杂物会诱导幂律数密度调制和流动。这些变化的形式不同，具体取决于夹杂物是否由外力（例如光学镊子）固定，或者是否是自由的。当夹杂物保持在原位时，远场流体流动是斯托克斯let，而微游泳器密度衰减为 1/r2+ε，其中 r 是与夹杂物的距离，ε是一个异常指数，它取决于夹杂物的对称性，并作为表征对流和扩散效应相对振幅的无量纲数的函数连续变化。角度依赖性采用非平凡形式，它依赖于相同的无量纲数。当夹杂物可以自由移动时，远场流体流动是应力小的，微游泳器密度衰减为 1/r2，具有简单的角度依赖性。这些长程调节介导我们表征的内含物之间的长程相互作用。