  A liquid film wetting the interior of a long circular cylinder redistributes
under the action of surface tension to form annular collars or occlusive plugs.
These equilibrium structures are invariant under axial translation within a
perfectly smooth uniform tube and therefore can be displaced axially by very
weak external forcing. We consider how this degeneracy is disrupted when the
tube wall is rough, and determine threshold conditions under which collars or
plugs resist displacement under forcing. Wall roughness is modelled as a
non-axisymmetric Gaussian random field of prescribed correlation length and
small variance, mimicking some of the geometric irregularities inherent in
applications such as lung airways. The thin film coating this surface is
modelled using lubrication theory. When the roughness is weak, we show how the
locations of equilibrium collars and plugs can be identified in terms of the
azimuthally averaged tube radius; we derive conditions specifying equilibrium
collar locations under an externally imposed shear flow, and plug locations
under an imposed pressure gradient. We use these results to determine the
probability of external forcing being sufficient to displace a collar or plug
from a rough-walled tube, when the tube roughness is defined only in
statistical terms.
