Thermocapillary Instabilities in Liquid Metals: Hartmann Number Versus Prandtl-Number

The technical need for instability postponement, turbulence suppression and flow control in material processing as well as the seek for low-cost alternatives to space-technologies for crystal growth are currently leading to an increased interest in the interaction between thermocapillary flows in electrically conducting fluids and magnetic fields. While the interplay between isothermal flows and magnetic fields is well understood, our physical understanding of the influence of magnetic fields on thermocapillary flow phenomena, i.e. flows driven by surface tension gradients, leaves still much to be desired.
The goal of the püresent communication is to demonstrate that a magnetic field acting on the thermocapillary flow of a low Prandtl number fluid causes the fluid to behave like a high Prandtl number fluid. This important feature is exemplified by considering the linear stability of a unidirectional thermocapillary flow set up by a temperature gradient parallel to the free surface of an unbounded planar fluid layer. The magnetic field is supposed to be normal to the free surface. Our problem is the magnetic counterpart to the work of Smith & Davis. We report results of a comprehensive study of the critical Marangoni number for the onset of hydrothermal waves as a function of the Hartmann number and of the Prandtl number. For weak magnetic field the instability mechanism in liquid metals is found to be the same as in the nonmagnetic case for low Prandtl numbers. For sufficiently strong magnetic field the basic flow and the most unstable perturbation are confined to a thin Hartmann boundary layer below the free surface which leads to a decrease of the effective viscous diffusion time-scale as Ha-2. Our Computations reveal that at a certain value of the Hartmann number, when the effective viscous time equals the thermal diffusion time, the character of the instability changes discontinously. The new type of instability is reminiscent of the instability mechanism w ...