Pairwise interactions of active particles in a yield stress fluid

In this work, we numerically investigate the hydrodynamic interactions between two active particles (modeled as squirmers) in a Bingham yield stress fluid, and quantify the influence of the Bingham number and squirmer type on reorientation and scattering in face-to-face and crossing configurations. In the face-to-face configuration, increased Bingham number leads to greater reorientation of neutral and puller-type squirmers. In crossing interactions, yield stress suppresses the strong deflection observed in Newtonian fluids at small incidence angles. In contrast, for larger initial angles, the final separation angle between the squirmers is significantly increased in a yield stress fluid compared to that in a Newtonian fluid. To elucidate the underlying mechanism, we compute hydrodynamic torques on particles by constraining their orientations while allowing translation. In the face-to-face configuration, we find that yield stress amplifies the near-field torques on each particle, driving them to rotate away from one another and thereby increasing scattering. In the side-by-side configuration, yield stress qualitatively alters the sign and magnitude of the hydrodynamic torque on neutral and puller-type squirmers, reducing their tendency to rotate away and thereby favoring sustained parallel swimming. These results provide insight into the rheological behavior and transport properties of active suspensions in complex fluids.