  For active particles the interplay between the self-generated hydrodynamic
flow and an external shear flow, especially near bounding surfaces, can result
in a rich behavior of the particles not easily foreseen from the consideration
of the active and external driving mechanisms in isolation. For instance, under
certain conditions, the particles exhibit "rheotaxis," i.e., they align their
direction of motion with the plane of shear spanned by the direction of the
flow and the normal of the bounding surface and move with or against the flow.
To date, studies of rheotaxis have focused on elongated particles (e.g.,
spermatozoa), for which rheotaxis can be understood intuitively in terms of a
"weather vane" mechanism. Here we investigate the possibility that spherical
active particles, for which the "weather vane" mechanism is excluded due to the
symmetry of the shape, may nevertheless exhibit rheotaxis. Combining analytical
and numerical calculations, we show that, for a broad class of spherical active
particles, rheotactic behavior may emerge via a mechanism which involves
"self-trapping" near a hard wall owing to the active propulsion of the
particles, combined with their rotation, alignment, and "locking" of the
direction of motion into the shear plane. In this state, the particles move
solely up- or downstream at a steady height and orientation.
