Hydrodynamic instabilities in thermocapillary flows

A review is given on the first convective instabilities of steady axisymmetric thermocapillary flows in models of the float-zone process. The commonly used model is briefly formulated and its limitations are addressed. The discussion concentrates on results obtained for the so-called half-zone model. The influence of Reynolds- (Marangoni-), Prandtl-, Biot-, and the Grashof number, as well as the aspect ratio on the stability boundary is discussed. The instability for large Prandtl numbers is of hydrothermal wave type in analogy to plane layers. At small Prandtl numbers, however, the first instability is stationary. Due to the scatter of the available results calculations with higher accuracy would be useful to set some bench marks. The reliability of results from fast numerical codes suitable to explore the parameter space in more detail could thus be tested.