Linear stability analysis on the thermocapillary flow of molten silicon in a liquid bridge between unequal disks under a rotating magnetic field

Abstract

This paper explores the stability of thermocapillary flow in a molten silicon liquid bridge situated between two unequal disks and subjected to a rotating magnetic field. Two different heating strategies are examined, and the static deformation of the free surface is taken into account by solving the Young–Laplace equation. Using linear stability analysis based on the Legendre spectral element method, the critical conditions are determined, and the underlying instability mechanism is uncovered through energy analysis. When heated from the bottom disk, three transitions between axisymmetric steady flow and three-dimensional oscillatory flow are observed within a narrow range of 7000 ≤ Ta ≤ 9000. In contrast, when heated from the top disk, the rotating magnetic field significantly enhances the flow stability. Furthermore, based on the energy analysis, we identify two types of instability caused by purely hydrodynamic mechanisms.