General aspects of hydrodynamic interactions between three-sphere low-Reynolds-number swimmers

We investigate hydrodynamic interactions between two three-sphere swimmers analytically and numerically. Hydrodynamic forces exerted on the swimmers as well as the translational and angular velocities of them are obtained in the far field regime. We demonstrate that the active term of the translational velocity is along the intrinsic direction of swimming (n) and has no component along the direction of relative positions of swimmers (r[over ̂]) as reported in previous papers. Using numerical simulations we investigate the long-time swimming paths of swimmers in two general situations of swimming in the same and opposite directions. The former reveals four swimming states for symmetric swimmers-attractive, repulsive, parallel, and oscillatory-and only three swimming states for asymmetric swimmers-attractive, repulsive, and contracting-oscillatory, confirming that the expanding-oscillatory state reported in previous papers is not stable. The latter shows that there are rotative bound states in hydrodynamic scattering of the swimmers.