Thermocapillary suppression of the Plateau–Rayleigh instability: a model for long encapsulated liquid zones

Abstract

A cylindrical liquid bridge is unstable when its length is longer than its circumference, the Plateau–Rayleigh limit. This capillary instability is modified by fluid motions adjacent to the interface, which can be induced by thermocapillary stress, among other means. A simple flow model with symmetry that mimics the situation in encapsulated floating zones is analysed. The interfacial balance equation is formulated as a bifurcation problem, appropriate when the flows are nearly rectilinear. This balance captures the competition between capillary stress and the flow-induced pressure. The fluid motions are shown to have a stabilizing effect; bridges much longer than the classical limit are stabilized. Numerical branch-tracing and the Lyapunov–Schmidt reduction methods provide the bifurcation structures of branching solutions. A normal-form analysis predicts standing-wave patterns due to mode–mode interaction. The model is proposed as an explanation for the extra long float zones observed in various spacelab experiments.