  This work analyzes the viscous flow and elastic deformation created by the
forced axial motion of a rigid cylinder within an elastic liquid-filled tube.
The examined configuration is relevant to various minimally invasive medical
procedures in which slender devices are inserted into fluid-filled biological
vessels, such as percutaneous revascularization, interventional radiology,
endoscopies and catheterization. By applying the lubrication approximation,
thin shell elastic model, as well as scaling analysis and regular and singular
asymptotic schemes, the problem is examined for small and large deformation
limits (relative to the gap between the cylinder and the tube). At the limit of
large deformations, forced insertion of the cylinder is shown to involve three
distinct regimes and time-scales: (i) initial shear dominant regime, (ii)
intermediate regime of dominant fluidic pressure and a propagating
viscous-peeling front, (iii) late-time quasi-steady flow regime of the fully
peeled tube. A uniform solution for all regimes is presented for a suddenly
applied constant force, showing initial deceleration and then acceleration of
the inserted cylinder. For the case of forced extraction of the cylinder from
the tube, the negative gauge pressure reduces the gap between the cylinder and
the tube, increasing viscous resistance or creating friction due to contact of
the tube and cylinder. Matched asymptotic schemes are used to calculate the
dynamics of the near-contact and contact limits. We find that the cylinder
exits the tube in a finite time for sufficiently small or large forces.
However, for an intermediate range of forces the radial contact creates a
steady locking of the cylinder inside the tube.
