  We investigate the effect of three important processes by which AGN-blown
bubbles transport material: drift, wake transport and entrainment. The first of
these, drift, occurs because a buoyant bubble pushes aside the adjacent
material, giving rise to a net upward displacement of the fluid behind the
bubble. For a spherical bubble, the mass of upwardly displaced material is
roughly equal to half the mass displaced by the bubble, and should be ~
10^{7-9} solar masses depending on the local ICM and bubble parameters. We show
that in classical cool core clusters, the upward displacement by drift may be a
key process in explaining the presence of filaments behind bubbles. A bubble
also carries a parcel of material in a region at its rear, known as the wake.
The mass of the wake is comparable to the drift mass and increases the average
density of the bubble, trapping it closer to the cluster centre and reducing
the amount of heating it can do during its ascent. Moreover, material dropping
out of the wake will also contribute to the trailing filaments. Mass transport
by the bubble wake can effectively prevent the build-up of cool material in the
central galaxy, even if AGN heating does not balance ICM cooling. Finally, we
consider entrainment, the process by which ambient material is incorporated
into the bubble. Abridged
