Equilibrium configurations of drops or bubbles in an eccentric annulus

Abstract

The purpose of this paper is to find the zero-gravity equilibrium configurations of liquid drops or bubbles that have sufficient volume to form large-aspect-ratio bridging segments or occluding slugs in the eccentric annulus between two cylinders. In zero gravity, the static problem depends on the contact angle of the fluid segment on the solid support, and two geometric parameters: the radius ratio and the dimensionless distance between the cylinder centres. For both non-wetting and wetting liquids, we find regions of geometric parameter space where only occluding configurations occur, a bistable region where either configuration can occur, and a region where only the non-occluding bridging configuration can occur. For the non-occluding cases, we applied a large-aspect-ratio free-energy minimization approach to predict the cross-sectional shape of the liquid, and a finite element method was used to compute the interface shape of the occluding cases. A Surface Evolver model was used to simulate the three-dimensional shape of both occluding and non-occluding configurations. The simulation results support the theoretical predictions well. The fractional open area of the conduit was determined for both highly wetting and highly non-wetting minority phases. Optimization of the geometric parameters for a given wetting condition could facilitate the segregation and transport of two fluid phases in applications involving large aspect ratios and small pressure driving forces.