THERMOCAPILLARY STABILIZATION OF THE CAPILLARY BREAKUP OF AN ANNULAR FILM OF LIQUID

It is known that the breakup by surface tension of a cylindrical interface containing a viscous liquid can be damped by axial motion of the underlying liquid and that for an annular film the capillary instability can be completely suppressed (disturbances of all wavelengths decay) by certain axial velocity profiles. Here, using a linear stability analysis, it is shown that complete stabilization can also occur for thermocapillary-driven axial motions. However, the influence of thermocapillary instabilities typically shrinks the window in parameter space where stabilization is found, relative to the isothermal case. The influence of Reynolds, surface tension, Prandtl, and Biot parameters on limits of stabilization is calculated using continuation techniques. It is observed that windows of stabilization first open with topological changes of the neutral curves in parameter space. A long-wave analysis unfolds the nature of the singularities responsible for several of these topological changes. The analysis also leads to the physical mechanism responsible for (long-wave) stabilization and in certain cases to necessary conditions for (long-wave) stabilization.