Pattern formation of thermocapillary flows in liquid bridges

The non-intrusive measurement of velocity and temperature fields inside liquid metals is very difficult owing to their opacity for light in the near-visible range and the lack of suitable tracer particles. This is one of the reasons why numerical modeling of liquid metal how has become increasingly important, in particular in crystal growth from the melt. Apart from the desire to model technical processes as realistically as possible, simple model studies have been carried out to investigate the fundamental fluid physics. These simple models are also very valuable for the test and the development of velocity-measurement techniques using, e.g. X-rays. This paper reports on recent advancements in the numerical analysis of thermocapillary how in the most wide-spread model for the float-zone process of silicon crystal growth. In the model, tangential free surface forces drive a toroidal vortex how inside a cylindrical volume of liquid. On an increase of the driving shear stresses induced by thermocapillarity the flow undergoes a sequence of pattern forming instabilities. The properties of these transitions, which are quite different for transparent high- and opaque low-Prandtl-number fluids, the physical mechanisms, and the structure of the associated how fields will be addressed. Results have been obtained by three-dimensional linear stability analyses and full numerical simulations of the governing equations.