Linear stability analysis of thermocapillary convection in liquid bridges and the energy budget of neutral perturbations

As a model for the floating-zone technique the thermocapillary flow in a noncylindrical axisymmetric liquid bridge is investigated numerically. The stationary 2D flow can become 30 and/or oscillatory at high thermocapillary Reynolds numbers, depending on the Prandtl number. The critical points are determined by a linear stability analysis and the instability mechanisms are investigated by a posteriori energy balances of the perturbations. In particular, the influence of the liquid bridge's shape on the linear stability boundary and on the mechanisms is analyzed. A is shown that on Me one side the principal instability mechanisms do not depend on the liquid bridge's shape but on the other side it influences the critical azimuthal wave number.