Anomalous Long-Ranged Influence of an Inclusion in Momentum-Conserving Active Fluids

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.