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

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.