Motion and mixing for multiple ferromagnetic microswimmers

This paper concerns the interaction of several ferromagnetic microswimmers, their motion and the resulting fluid mixing. Each swimmer consists of two ferromagnetic beads joined by an elastic link, and is driven by an external, time-dependent magnetic field. The external field provides a torque on a swimmer and, together with the varying attraction between the magnetic beads, generates a time-irreversible motion leading to persistent swimming in a low Reynolds number environment. The aim of the present paper is to consider the interactions between several swimmers. A regime is considered in which identical swimmers move in the same overall direction, and their motion is synchronised because of driving by the external field. It is found that two swimmers tend to encircle one another while three undergo more complicated motion that may involve the braiding of swimmer trajectories. By means of approximations it is established that the interaction between pairs of swimmers gives circulatory motion which falls off with an inverse square law and is linked to their overall speed of motion through the fluid. As groups of two or more swimmers move through the fluid they process fluid, leaving behind a trail of fluid that has undergone mixing: this is investigated by following streak lines numerically.