Numerical Simulations of Thermocapillary Flow of a Binary Mixture with the Soret Effect in a Shallow Annular Pool

In order to understand the characteristics of thermocapillary flow of a toluene/n-hexane mixture with the Soret effect in a shallow annular pool, a series of three-dimensional numerical simulations were carried out. The shallow annular pool was heated from the outer cylinder and cooled at the inner cylinder. The initial toluene concentration in the toluene/n-hexane mixture varied from 0 to 0.4467. Results indicate that the flow undergoes two transitions from the axisymmetric steady flow to the hydrothermal waves, and then to chaos with the increase of the thermocapillary Reynolds number. The critical thermocapillary Reynolds number for the incipience of the oscillatory flow decreases with the increase of the initial solute concentration. When the thermocapillary flow transits to a three-dimensional oscillatory flow, a concentration fluctuation is observed on the free surface, which is similar to the hydrothermal waves. However, compared with that of the temperature, the dimensionless fluctuation amplitude of the concentration is relatively weak. Furthermore, the fundamental oscillation frequency increases linearly with the initial solute concentration, but the wave number of the hydrothermal waves is almost unchangeable.