  In both biological and artificial systems, concentration gradients can serve
as a convenient mechanism for manipulating particles and generating motility.
Particles that interact with a solute will move along its gradient; if they
themselves generate the gradient, this mechanism provides a means of
self-propulsion. We consider a version of this type of motility appropriate to
certain biological systems where polymeric filaments provide the concentration
gradient. As the filament diffusion is small, this corresponds to a regime of
large P\'eclet number where the motion is dominated by the effects of fluid
advection. The nature of such concentration-gradient-driven motion in the
advective regime differs in certain fundamental respects from the same process
at low P\'eclet number. In particular, we show that out of four broad scenarios
of steady state motion at low P\'eclet number, only two remain viable in the
strongly advecting limit.
