  Motivated by recent experiments [Science {\bf 299}, 1042 (2003)] reporting
that carbon nanotubes immersed in a flowing fluid displayed an electric current
and voltage, we numerically study the behaviour of a collection of Brownian
particles in a channel, in the presence of a flow field applied on similar but
slower particles in a wide chamber in contact with the channel. For a suitable
range of shear rates, we find that the flow field induces a unidirectional
drift in the confined particles, and is stronger for narrower channels. The
average drift velocity initially rises with increasing shear rate, then shows
saturation for a while, thereafter starts decreasing, in qualitative agreement
with recent theoretical studies [Phys. Rev. B {\bf 70}, 205423 (2004)] based on
Brownian drag and ``loss of grip''. Interestingly, if the sign of the
interspecies interaction is reversed, the direction of the induced drift
remains the same, but the flow-rate at which loss of grip occurs is lower, and
the level of fluctuations is higher.
