A singularity model for the dynamics of externally driven microswimmers

In recent years, artificial microswimmers have received significant research attention due to their potential biomedical and engineering applications. The propulsion of magnetic micro-robots by an external magnetic field seems particularly promising, as it presents the capability to control these swimmers remotely. Specifically the dynamics of magnetic microswimmers composed of spheres have recently been explored, as these geometries are easily experimentally realized and may be configured to possess the necessary asymmetries to couple a translational motion to an external torque.

In this talk we present a simplified Stokes singularity based model for such microswimmers. This model allows the investigation of the interaction of such swimmers with walls and other microswimmers.  While singularity models have become commonplace in the mathematical modeling of biological locomotion, these methods have not been readily used for the modeling of these externally driven swimmers, in part due to the difficulty of computing the time-varying singularity strengths. We expect that the proposed singularity models will have applications in the development of control strategies for externally driven teams of micro-robots and path planning in the presence of complex boundaries.