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This work analyzes the viscous flow and elastic deformation created by theforced axial motion of a rigid cylinder within an elastic liquid-filled tube.The examined configuration is relevant to various minimally invasive medicalprocedures in which slender devices are inserted into fluid-filled biologicalvessels, 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 singularasymptotic schemes, the problem is examined for small and large deformationlimits (relative to the gap between the cylinder and the tube). At the limit oflarge deformations, forced insertion of the cylinder is shown to involve threedistinct regimes and time-scales: (i) initial shear dominant regime, (ii)intermediate regime of dominant fluidic pressure and a propagatingviscous-peeling front, (iii) late-time quasi-steady flow regime of the fullypeeled tube. A uniform solution for all regimes is presented for a suddenlyapplied constant force, showing initial deceleration and then acceleration ofthe inserted cylinder. For the case of forced extraction of the cylinder fromthe tube, the negative gauge pressure reduces the gap between the cylinder andthe tube, increasing viscous resistance or creating friction due to contact ofthe tube and cylinder. Matched asymptotic schemes are used to calculate thedynamics of the near-contact and contact limits. We find that the cylinderexits the tube in a finite time for sufficiently small or large forces.However, for an intermediate range of forces the radial contact creates asteady locking of the cylinder inside the tube.

Forced motion of a cylinder within a liquid-filled elastic tube