Free surface shear flows induced by Marangoni and alternating electromagnetic forces

One of the effects of radio-frequency (RF) alternating magnetic fields generated in the vicinity of electrically conducting liquid components is the generation of a free surface shear flow. This effect is generally undesired, but could be used to improve convection control in some applications - such as the Czochralski or floating zone crystal growth processes for example. Since the low value of the magnetic skin depth most often leads to high numerical difficulties, we have developed a mathematical model for the electromagnetic field distribution in the conductors for axisymmetric configurations, which provides equivalent magnetic surface forces and heat flux. The choice of an appropriate inductor shape, and the use of several out-of-phase induction components, allows us to equalize the orders of magnitude of tangential electromagnetic and thermocapillary Marangoni forces. In such case, the electromagnetic field can be used to counteract the Marangoni effect and to control the flow. Numerical calculations of the convection induced by electromagnetic and thermocapillary forces are carried out in order to depict typical flow patterns obtained in an axisymmetric liquid bridge surrounded by inductors