Instabilities of Thermocapillary Flows between Counter-rotating Disks

Thermocapillary flows are important in many applications, such as the floating-zone and Czochralski crystal growth techniques. In production of crystals by the floating zone method, the feed and crystal rods are often rotating in order to suppress the azimuthal asymmetry. We perform the linear stability analysis of the thermocapillary flows between counter-rotating disks. The basic flow and temperature solutions are obtained by using the pseudo-spectral Chebyshev method. The perturbation equations are solved with Chebyshev polynomial expansions in the radial and vertical directions. When no rotation is applied, the instability depends on the Prandtl number. For small Prandtl number liquids (Pr &l