Zero-gravity liquid-vapor interfaces in circular cylinders

Abstract

The zero-gravity problems of a liquid volume sealing a circular tube of gas and a gaseous volume in a circular tube of liquid both involve one phase obstructing another. The two problems differ only in contact angle. From pulmonary research there is a history of axisymmetric analyses for liquid droplets in circular tubes of gas. These analyses consider only axisymmetric solutions-an annulus and an axisymmetric plug. Only recently have nonsymmetric solutions for nonzero contact angle wetting liquids ͑0°-90°contact angle͒ been realized by the authors with the use of the Surface Evolver code. Similar to the problem of droplets in a gas filled tube, a bubble in a liquid-filled tube is of interest to the commercial satellite industry and in vascular physiology. Further analysis by the authors now fills in the other half of contact angle range, i.e., either a nonwetting liquid in a tube of gas ͑contact angles of 90°-180°͒, or equivalently, a gaseous bubble in a liquid that wets the tube wall. Conditions for the existence and stability of solutions of three topologies are examined.

The influence of channel wettability and geometry on water plug formation and drop location in a proton exchange membrane fuel cell flow field

“…The minimum liquid volume required for a plug to exist is investigated. This is similar to recent studies on the stability of drops and plugs in tubes [25,26] and the more general formulation for the existence (and nonexistence) of liquid occlusion in arbitrary tubes under transverse gravitational fields [27]. This study examines the minimum volume required for a plug to exist in channels with planar walls having different wettabilities.…”

Occlusion criteria in tubes under transverse body forces

“…In a cylinder of arbitrary cross-section, a variety of interface configurations may exist under weightless conditions, which may or may not occlude or block the entire cross-section (Collicott, Lindsley and Frazer 2006). If a body force is then applied, blockage may or may not occur, depending on the force and on how it is applied.…”

Wetting of a liquid annulus in a capillary tube

“…In this context, an exact analytical solution for the interface profile was found (15)(16)(17)(18). There is extensive literature on the stability of cylindrical liquid surfaces (3,(19)(20)(21)(22)(23)(24)(25)(26)(27). An infinitely extended liquid cylinder is always unstable under perturbations of sufficiently long wavelength (28).…”

“…He analyzed the evolution of structures such as collars and plugs. Based on the finite-element method, Collicott (25) studied the possible morphologies of a liquid in a circular tube without gravity at all contact angles ranging from 0° to 180°. They especially focused on non-axisymmetric configurations.…”

“…One challenge is to find a sufficiently general solution of the Young-Laplace equation for the stable static equilibrium configuration and to determine the critical parameters of the instability. In that context, up to now analytical solutions were obtained for some complete wetting states (19,20), or numerical methods (22,24,25,27) were employed, or the conclusions were built on approximations (21) in which the radial coordinate of the liquid surface is supposed to be some function of the axial coordinate. The objective of the present paper is the solution of the Young-Laplace equation for an axisymmetric liquid volume at zero gravity in a cylindrical capillary with an arbitrary contact angle.…”