Search Results (4)

During the crystal growth process using the floating zone method, the uneven distribution of impurities on the surface of the melt can trigger a coupling mechanism between solutocapillary convection driven by the concentration gradient and thermocapillary convection driven by the temperature gradient, resulting in the Marangoni convection at the free surface. When the temperature and concentration gradients reach certain values, the crystal surface and interior exhibit time-dependent, periodic oscillations, leading to the formation of micrometer-scale impurity stripes within the crystal. This study focuses on the effects of temperature difference and heat loss in a liquid bridge under microgravity on the structure and interface oscillation characteristics of thermo-solutocapillary convection, aiming to explore the coupling phenomenon of this oscillation and provide valuable information for crystal growth processes. An improved level set method is employed to accurately track every displacement of the interface, while the surface tension is addressed using the CSF model. In addition, the area compensation method is used to maintain simulation quality balance. A comprehensive analysis is performed on the oscillation characteristics of thermo-solutocapillary convection at the free surface, ranging from the temperature, concentration, deformation, and velocity distributions at the upper and middle heights of the liquid bridge. The results indicate that under small temperature differences (ΔT = 1 − 3), the transverse velocity at the upper end exhibits a single-periodic oscillation, while the longitudinal velocity presents a double-periodic oscillation. At the intermediate height, both the transverse and longitudinal velocities display a single-periodic oscillation. Under a large temperature difference (ΔT = 6), the oscillation of velocities at the upper end and the middle position become multi-periodic. In addition, heat loss has certain regular effects on the oscillatory flow of thermo-solutocapillary convection within a certain range. The velocity, amplitude, and frequency of the upper end and the middle position at the free surface decrease gradually, and the oscillation intensity also weakens with the increase in heat loss (Bi = 0.2 − 0.6). These new discoveries can provide a valuable reference for optimizing the crystal growth process, thereby enhancing the quality and performance of crystal materials. Full article

A numerical simulation has been conducted to investigate the oscillatory mechanism of a solutocapillary convection and the influence of different aspect ratios on the flow characteristics in a liquid bridge. The SIMPLE algorithm is applied to figure out the Navier-Stokes equation and the concentration diffusion equation on the staggered grids, and the level set approach with the conservation of the mass is used to acquire the surface deformation of the liquid bridge. The flow characteristics of the oscillatory solutocapillary convection are analyzed in detail, including the distributions of the concentration, velocity, and transverse displacement of the free surface at the upper corner and intermediate height of the liquid bridge. Moreover, the effects of the aspect ratio on the flow stability and onset time of the oscillations for the concentration and velocity have also been investigated. The results show that the essence of the oscillatory solutocapillary convection is the result of the coupling oscillation of the concentration, velocity and free surface. The upper corner is the origin region of the oscillation, which has an important impact on the overall flow characteristics. Within a definite height range of the liquid bridge, the lower the height, the more stable the flow and the weaker the oscillation. There is a complex relationship between the onset time of the concentration and velocity oscillations and the aspect ratio of the liquid bridge. Full article

This paper investigated the influence of surface internal energy instability caused by the gravitational tilt angle on solutocapillary convection. The results showed that the spatio-temporal evolution of solutocapillary convection in a non-axisymmetric liquid bridge was divided into three stages under different gravitational tilt angles, “the initiating stage near the upper corner”, “development to the intermediate height”, and “shrinking toward the bottom corner”. The non-equilibrium of the left or right interface curvature caused by internal energy instability promotes the distortion of the cell flow structure. The concentration gradient on the far-earth side increases first, due to the gravitational tilt angle. With the increasing gravitational tilt angle, the lateral extension of the cell flow is inhibited. The transverse/longitudinal velocity components are suppressed; however, the velocity gradient near the boundary is increased, and the uniformity of the velocity distribution in the center of the liquid bridge is improved. The axial component of the Bond number decreases in a small range (Bo′ = 1→0.98) with the internal energy instability, however, which has a significant effect on surface flow. Therefore, in the initiation and development stages of solutocapillary convection, the decay rate of the Marangoni number respectively decreases and increases with the increasing Bond number. The axial component of the Bond number decreases in a small range with the internal energy instability, which has a significant effect on the solute Marangoni number (Ma_c). In the initiation stage of solutocapillary convection, the decay rate of the Ma_c decreases with the increasing Bond number. Its change law is the opposite in the development stage of solutocapillary convection. Full article

This work presented a series of three-dimensional unsteady numerical simulations on the characteristics of the mixed oscillation flows of binary mixture in a Czochralski crystal growth model. The silicon-germanium melt is investigated and the capillary ratio is minus one. The simulation results showed that, for the special capillary ratio, the thermal and solutocapillary forces are imposed in opposite directions and counteract each other. With the effect of buoyancy, the balance between the capillary forces is disturbed. Mixed with the forced convection driven by rotation, the capillary-buoyancy convection is complex. The basic mixed flow streamlines are presented as various rolling cells. The directions of the rolls are dependent on the combinations of surface and body forces. With the increase of temperature gradient, the basic flow stability is broken, and the oscillations occur. The crucible rotation has an effective influence on the stability enhancement. However, affected by the crystal rotation, the critical condition experiences an increase to a turning point, and then undergoes a sharp reduction to zero. Once the instability is incubated, the surface oscillations are analyzed. For the three-dimensional steady flow, only spatial oscillations are observed circumferentially, and the surface patterns of spokes, rosebud, and pulsating ring are obtained. For the unsteady oscillation flow, the spiral hydrosoultal waves, rotating waves, and superimposition of spirals and spokes are observed, and the oscillation behaviors are also discussed. Full article