Influence of the volume of liquid on the onset of three-dimensional flow in thermocapillary liquid bridges

The stability of axisymmetric flow in thermocapillary liquid bridges is investigated by a linear stability analysis using a finite-difference method. We consider the case when the static meniscus is non-cylindrical depending on the volume of liquid contained in the bridge. Neglecting dynamic free-surface deformations (zero-Capillary-number limit) the deformed domain occupied by the liquid is mapped onto a cylindrical volume by a coordinate transformation. We present critical Reynolds numbers, compare with previously published data, and discuss the influence of the free-surface deformation on the instability mechanism.