# Dynamics of a liquid plug in a capillary tube under cyclic forcing: memory effects and airway reopening

## TL;DR

This study explores how cyclic forcing affects liquid plug dynamics in capillary tubes, revealing memory effects, stability conditions, and potential for airway reopening, supported by experiments and analytical modeling.

## Contribution

It introduces a comprehensive analysis of cyclic forcing on liquid plugs, highlighting memory effects and instability mechanisms, with a validated analytical model for predicting behavior.

## Key findings

- Cyclic forcing can stabilize or destabilize liquid plug motion.
- Memory effects influence resistance changes during cyclic forcing.
- Cyclic forcing can break large plugs, aiding airway reopening.

## Abstract

In this paper, we investigate both experimentally and theoretically the dynamics of a liquid plug driven by a cyclic periodic forcing inside a cylindrical rigid capillary tube. First, it is shown that depending on the type of forcing (flow rate or pressure cycle), the dynamics of the liquid plug can either be stable and periodic, or conversely accelerative and eventually leading to the plug rupture. In the latter case, we identify the sources of the instability as: (i) the cyclic diminution of the plug viscous resistance to motion due to the decrease in the plug length and (ii) a cyclic reduction of the plug interfacial resistance due to a lubrication effect. Since the flow is quasi-static and the forcing periodic, this cyclic evolution of the resistances relies on the existence of flow memories stored in the length of the plug and the thickness of the trailing film. Second, we show that contrary to unidirectional pressure forcing, cyclic forcing enables breaking of large plugs in confined space though it requires longer times. All the experimentally observed tendencies are quantitatively recovered from an analytical model. This study not only reveals the underlying physics but also opens up the prospect for the simulation of "breathing" of liquid plugs in complex geometries and the determination of optimal cycles for obstructed airways reopening.