Effect of rotating magnetic field on the stability of thermocapillary flow in a gallium arsenide liquid bridge between unequal ends

Abstract

In this study, we investigated the impact of a rotating magnetic field on the stability of a thermocapillary flow in a gallium arsenide liquid bridge (Prandtl number Pr = 0.068) situated between two unequal disks, considering two different scenarios with radius ratios of Γr = 0.98 and Γr = 0.60 for the upper heated disk. By utilizing linear stability analysis based on the Legendre spectral element method, we first identified the critical parameters of the onset of flow instability, including critical Marangoni number (Mac), dimensionless oscillation frequency (fc), and azimuthal wavenumber (m). Then, we employed kinetic energy budget analysis to uncover the underlying instability mechanism. For radius ratio Γr = 0.98, three transitions between axisymmetric steady flow and three-dimensional oscillatory flow in the narrow range of Taylor number Ta (8700≤Ta ≤ 9500) are observed; these transitions arise due to the interplay between the flow induced by rotating magnetic field and thermocapillary flow. For the Γr = 0.60 scenario, the rotating magnetic field is observed to significantly enhance the flow stability. Additionally, our analysis identifies four instability types dominated by the hydrodynamic mechanism. In the meantime, the thermocapillary mechanism also contributes to flow instability in the specific region of Taylor number Ta (1250≤Ta ≤ 8000) for radius ratio Γr = 0.98.