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

## TL;DR

This study models the viscous flow and elastic deformation caused by forcing a cylinder through an elastic tube filled with liquid, revealing regimes of motion, contact dynamics, and conditions for locking or exit.

## Contribution

It introduces a comprehensive analysis of cylinder motion in elastic tubes, including regimes, asymptotic solutions, and contact effects, relevant to medical device insertion.

## Key findings

- Identifies three deformation regimes during forced insertion.
- Derives a uniform solution for sudden force application.
- Shows conditions for cylinder exit or locking within the tube.

## Abstract

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.