Characterization of the thermal and solutal Marangoni flows of opposite directions developing in a cylindrical liquid bridge under zero gravity

Numerical simulations of the thermo-solutal Marangoni convection developing in a Si-Ge liquid bridge of a floating-zone system have been performed under zero gravity. Half of the liquid bridge was considered as the three-dimensional (3D) computational domain. In this system, the solutal Marangoni convection develops in the direction opposite to the thermal Marangoni convection along the free surface in the bridge, i.e., the thermal Marangoni number, Ma_T, is negative and the solutal Marangoni number, Ma_C, is positive. Since the SiGe melt is a low-Prandtl number (Pr = 6.37 × 10^-3) and high-Schmidt number (Sc = 14.0) liquid, the temperature field is almost independent of the convective flow and the concentration field determines the transport structures. When Ma_C is larger than -Ma_T, the concentration pattern is steady and two-dimensional (2D) axisymmetric. When Ma_C is smaller than -Ma_T, we predict two kinds of flow transitions with the increase in |Ma_T|. If Ma_C is sufficiently large (Ma_C ≳ 530), as |Ma_T| increases, the flow changes from a 2D-steady pattern to a 3D-chaotic behavior at moderate |Ma_T| (1050 ≲ |Ma_T| ≲ 2800). We also predict that a second transition and an oscillatory rotating flow occur as |Ma_T| increases further. The flow becomes 3D-steady at smaller Ma_C (Ma_C ≲ 360) with no transition, and the azimuthal wavenumber (m) decreases with increasing |Ma_T|. Furthermore, the thermo-solutal Marangoni convection in this system can be suppressed almost completely when Ma_C is approximately equal to -Ma_T (Ma_C ≈ -Ma_T) and the flow becomes periodically stable with weak fluctuations.