Bodies in an interacting active fluid: Far-field influence of a single body and interaction between two bodies

Because active particles break time-reversal symmetry, an active fluid can sustain currents even without an external drive. We show that when a passive body is placed in a fluid of pairwise interacting active particles, it generates long-range currents, corresponding to density and pressure gradients. By using a multipole expansion and a far-field constitutive relation, we show that the leading-order behavior of all three corresponds to a source dipole. Then, when two bodies or more are placed in the active fluid, generic long-range interactions between the bodies occur. We find these to be qualitatively different from other fluid mediated interactions, such as hydrodynamic or thermal Casimir. The interactions can be predicted by measuring a few single-body properties in separate experiments. Moreover, they are anisotropic and do not satisfy an action-reaction principle. These results extend previous results on non-interacting active particles. Our framework may point to a path towards self-assembly.