  In this study, we use numerical simulations to investigate the flow field
induced by a single magnetic microrobot rotating with a constant angular speed
about an axis perpendicular to an underlying surface. A parallel solver for
steady Stokes flow equations based on the boundary-element method is used for
simulating these flows. A simple transformation is introduced to extend the
predictive capability of the solver to cases with small unsteadiness. Flows
induced by four simple robot shapes are investigated: sphere, upright cylinder,
horizontally-laid cylinder, and five-pointed star-shaped prism. Shapes with
cross-sections that are axisymmetric about the rotation axis (sphere and
upright cylinder) generate time-invariant flow fields, which could be useful
for applications such as micromanipulation. Non-axisymmetric shapes
(horizontally-laid cylinder and the star-shaped prism) induce significant
unsteadiness inside the flow field, which could be desirable for applications
such as micromixing. Furthermore, a slender horizontally-laid cylinder
generates substantially three-dimensional flows, an added benefit for
micromixing applications. The presence of nearby walls such as a bottom
substrate or sidewalls has a retarding effect on the induced flows, which is
quantified. Finally, we present the driving torque and power-consumption of
these microrobots rotating in viscous liquids. The numerical modeling platform
used in this work can enable future optimal microrobot designs for a given
application requirement.
