Thermocapillary instabilities in a laterally heated liquid bridge with end wall rotation

• Published in: Physics of fluids (1994) 2011-10, Vol.23 (10), p.104104-104104-16
• Main Authors: Kahouadji, L., Houchens, B. C., Witkowski, L. Martin
• Format: Article
• Language: English
• Subjects: Cross-disciplinary physics: materials science; rheology; Exact sciences and technology; Fluid dynamics; Fluid mechanics; Fundamental areas of phenomenology (including applications); Growth from melts; zone melting and refining; Hydrodynamic stability; Materials science; Mechanics; Methods of crystal growth; physics of crystal growth; Physics; Surface-tension-driven instability
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.3644717

The effect of rotation on the stability of thermocapillary driven flow in a laterally heated liquid bridge is studied numerically using the full-zone model of the floating-zone crystal growth technique. A small Prandtl number (0.02) fluid, relevant for semiconductor melts, is studied with an aspect ratio (height to diameter of the melt) equal to one. Buoyancy is neglected. A linear stability analysis of three-dimensional perturbations is performed and shows that for any ratio of angular velocities, a weak rotation rate has the surprising effect of destabilizing the base flow. By systematically varying the rotation rate and ratio of angular velocities, the critical threshold and azimuthal wave number of the most unstable mode is found over a wide range of this two parameter space. Depending on these parameters, the leading eigenmode is a wave propagating either in the positive or negative azimuthal direction, with kinetic energy typically localized close to one of the end walls. These results are of practical interest for industrial crystal growth applications, where rotation is often used to obtain higher quality crystals.