Control of thermo- and solutocapillary flows in fz crystal growth by high-frequency vibrations

The paper deals with the numerical investigation of the possibilities to control convective flows in the liquid bridge in zero gravity conditions by applying axial vibrations. The surface tension is assumed to be dependent on both the temperature and solute concentration. The free surface deformations and the curvature of phase change surfaces are neglected but pulsating deformation of free surface are accounted for. The first part of the paper concerns axisymmetric steady flows. The calculations show that the evolution of convective flow with the variation of thermal Marangoni number at fixed value of the solutal Marangoni number is accompanied by the hysteresis phenomenon, which is related to the existence of two stable steady regimes in certain parameter range. One of these regimes is thermocapillary dominated, it corresponds to the two-vortex flow, and the other is solutocapillary dominated, it corresponds to the single-vortex flow. Under vibrational influence the range of hysteresis becomes narrower and is shifted to the area of larger Marangoni numbers. The second part of the paper concerns the stability of axisymmetric thermo- and solutocapillary flows and the transition to three-dimensional regimes. Significant mutual influence of flows generated by each of mechanisms on the stability of each other is discovered. Stability maps in the parameter plane thermal Marangoni number - solutal Marangoni number are obtained for different values of vibration parameters. It is shown, that vibrations exert a stabilizing effect due to increasing critical Marangoni numbers for all modes of instability. However, the character of this influence is different for different modes and at high intensity of vibrations destabilization is possible. Consequently, vibrations can modify a scenario of transition to three-dimensional modes.