Wetting of an annular liquid in a capillary tube

TL;DR

This paper analyzes the stability and morphology transitions of a liquid ring in a capillary tube, providing analytical solutions and numerical simulations to understand the conditions leading to stable, unstable, and non-axisymmetric configurations.

Contribution

It offers the first analytical solutions for the Young-Laplace equation for arbitrary contact angles in this context and maps the stability regimes of liquid morphologies.

Findings

Existence of two solutions with different stabilities for certain parameters.

Identification of critical parameters for transition to unstable configurations.

Numerical demonstration of the transition from axisymmetric to non-axisymmetric shapes.

Abstract

In this paper, we systematically investigate the wetting behavior of a liquid ring in a cylindrical capillary tube. We obtain analytical solutions of the axisymmetric Young-Laplace equation for arbitrary contact angles. We find that, for specific values of the contact angle and the volume of the liquid ring, two solutions of the Young-Laplace equation exist, but only the one with the lower value of the total interfacial energy corresponds to a stable configuration. The transition to an unstable configuration is characterized by specific critical parameters such as the liquid volume, throat diameter etc. Beyond the stable regime, the liquid ring transforms into a plug. Based on numerical simulations, we also discuss the transition of an axisymmetric ring into non-axisymmetric configurations. Such a transition can be induced by the Rayleigh-Plateau instability of a slender liquid ring. The results are presented in terms of a map showing the different liquid morphologies as a function of the parameters governing the problem.