  Biological microswimmers are known to navigate upstream of an external flow
(positive rheotaxis) in trajectories ranging from linear, spiral to
oscillatory. Such rheotaxis stems from the interplay between the motion and
complex shapes of the microswimmers, e.g. the chirality of the rotating
flagella, the shear flow characteristics, and the hydrodynamic interaction with
a confining surface. Here, we show that an isotropic, active droplet
microswimmer exhibits a unique oscillatory rheotaxis in a microchannel despite
its simple spherical geometry. The swimming velocity, orientation, and the
chemical wake of the active droplet undergo periodic variations between the
confining walls during the oscillatory navigation. Using a hydrodynamic model
and concepts of dynamical systems, we demonstrate that the oscillatory
rheotaxis of the active droplet emerges primarily from the interplay between
the hydrodynamic interaction of the finite-sized microswimmer with all the
microchannel walls, and the shear flow characteristics. Such oscillatory
rheotactic behavior is different from the directed motion near a planar wall
observed previously for artificial microswimmers in shear flows. Our results
provide a realistic understanding of the behaviour of active particles in
confined microflows, as will be encountered in majority of the applications
like targeted drug delivery.
