Effective interactions between inclusions in an active bath

We study effective two- and three-body interactions between non-active colloidal inclusions in an active bath of chiral or non-chiral particles, using Brownian dynamics simulations within a standard, two-dimensional model of disk-shaped inclusions and active particles. In a non-chiral active bath, we first corroborate previous findings on effective two-body repulsion mediated between the inclusions by elucidating the detailed non-monotonic features of the two-body force profiles, including a primary maximum and a secondary hump at larger separations that was not previously reported. We then show that these features arise directly from the formation, and sequential overlaps, of circular layers (or "rings") of active particles around the inclusions, as the latter are brought to small surface separations. These rings extend to radial distances of a few active-particle radii from the surface of inclusions, giving the hard-core inclusions relatively thick, soft, repulsive "shoulders," whose multiple overlaps then enable significant (non-pairwise) three-body forces in both non-chiral and chiral active baths. The resulting three-body forces can even exceed the two-body forces in magnitude and display distinct repulsive and attractive regimes at intermediate to large self-propulsion strengths. In a chiral active bath, we show that, while active particles still tend to accumulate at the immediate vicinity of the inclusions, they exhibit strong depletion from the intervening region between the inclusions and partial depletion from relatively thick, circular zones further away from the inclusions. In this case, the effective, predominantly repulsive interactions between the inclusions turn to active, chirality-induced, depletion-type attractions, acting over an extended range of separations.