Wetting of a liquid annulus in a capillary tube

Abstract

In this paper, we systematically investigate the static 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. Based on a numerical scheme determining configurations with a local minimum of the interfacial energy, we also discuss the stability limit between axisymmetric rings and non-axisymmetric configurations. Beyond the stable regime, a liquid plug or a sessile droplet exists instead of a liquid ring, depending on the values of the liquid volume and the contact angle. The stability limit is characterized by specific critical parameters such as the liquid volume, throat diameter, etc. The results are presented in terms of a map showing the different stable liquid morphologies that are obtained from an axisymmetric ring as base state.