An axisymmetric film bridge collapses under its own surface tension, disconnecting at a pair of pinchoff points that straddle a satellite bubble. The free-boundary problem for the motion of the film surface and adjacent inviscid fluid has a finite-time blowup (pinchoff). This problem is solved numerically using the vortex method in a boundary-integral formulation for the dipole strength distribution on the surface. Simulation is in good agreement with available experiments. Simulation of the trajectory up to pinchoff is carried out. The self-similar behaviour observed near pinchoff shows a ‘conical-wedge’ geometry whereby both principal curvatures of the surface are simultaneously singular – lengths scale with time as t2/3. The similarity equations are written down and key solution characteristics are reported. Prior to pinchoff, the following regimes are found. Near onset of the instability, the surface evolution follows a direction dictated by the associated static minimal surface problem. Later, the motion of the mid-circumference follows a t2/3 scaling. After this scaling ‘breaks’, a one-dimensional model is adequate and explains the second scaling regime. Closer to pinchoff, strong axial motions and a folding surface render the one-dimensional approximation invalid. The evolution ultimately recovers a t2/3 scaling and reveals its self-similar structure.
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.
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