Unusual Interfacial Phase Behavior of Two Nonmiscible Liquids in a Cylindrical Test Tube: Equilibrium Shapes and Stability of Axisymmetric Liquid Bridges under Gravity

Abstract

In this paper the unusual interfacial phase behavior of two nonmiscible fluids contained in a cylindrical glass test tube is reported. Water, which is the lighter phase, takes up the upper part of the tube, whereas the denser compound (a hydrofluorocarbon) is in the bottom. However, below some critical volume of water, the denser phase emerges at the air surface, by forming an axisymmetric liquid bridge through the aqueous phase. Above the critical condition, the formation of the bridge, the evolution of the shape of this bridge, and its final breakdown can be visually inspected after shaking the tube. The minority liquid (water) is dispersed in the majority phase (HCFC) as an unstable dispersion of droplets. Droplets rise to the air surface under the action of the buoyant force, and coalesce on the glass wall: this leads to the formation of a bridge (made from the dispersion in the middle of a hollow axisymmetric water drop), whose height increases and thickness decreases during the coalescence process, until it breaks down. Using a free energy analysis, we state the exact variational problem via its Euler–Lagrange equation. However, since this nonlinear differential equation cannot be solved analytically, a simplified “mean-field” approach is developed, which provides a comprehensive insight into the physical origin of these capillary bridges and their stability under gravity.