Study On The Capillary-Buoyancy Flow Of Binary Mixtures In An Annular Pool

The Czochralski crystal growth technology is one of the most frequently-employed methods for producing large scale crystals in the industry.The quality and scale of a crystal mainly depend on the flow of the melt.During the process of the Czochralski growth of binary crystals,there is a temperature difference between the crystal and crucible.In addition,as a result of the segregation and insoluble impurities,a solute concentration difference also exists between the crystal and crucible.When the temperature and solute concentration differences coexist on the free surface of the melt,the surface tension gradient generates,which drives the thremal capillary flow and solutal capillary flow.In the condition of the gravity,the density inhomogeneity due to the uneven distributions of the temperature and solute concertation induces the buoyancy flow.In order to meet the development of the technology in the industry,it is necessary to study melt flow driven by the coupling effects of thermal capillary flow,solutal capillary flow,thermal buoyancy flow and solutal capillary flow.In addition,it is essential to discuss the characteristics,instability and dissipative structure of the complex melt flow,which will help improve the controlling technology in the crystal growth process.It is of great academic significance to extend the thermocapillary flow from pure fluids to binary mixtures by studying the thermal-solutal capillary-bouyancy flow.In addition,it is possible to discover new flow patterns and instability mechanisms.In present work,a series of experiments and simulations were conducted to obtain the physical property parameters of several binary mixtures and study the capillary-buoyancy flow in binary mixtures.The flow structures,critical conditions for the evolution of flow patterns,flow field,temperature field,solute concentration field and destabilization mechanism are revealed.The main contents and results are as follows:(1)The 3S Mini Lab ILMS surface tension detector and TC 3010 L thermal conductivity tester were applied to obtain the surface tension,thermal conductivity,specific heat and so on of several binary mixtures,such as toluene/n-hexane,n-decane/n-hexane,benzene/n-heptane and so on,at different temperature and solute concentration.The liner regression method was used to deal with a great number of data from experiments to get the thermal expansion coefficient and solutal expansion coefficient of binary mixtures.The experimental results show that the temperature coefficients of surface tension of the n-decane/n-hexane,toluene/n-hexane,benzene/n-heptane and carbon tetrachloride/n-heptane mixtures are positive,while the solutal coefficients of surface tension of these mixtures are negative.Thus,the surface tensions of these mixtures decrease with the increasing temperature,but increase at a higher solute concentration.(2)Experiments and simulations were carried out to study the thermocapillary-buoyancy flow of binary mixtures with a moderate Prandtl number in an annular pool with the radial temperature gradient.The effects of the thermal capillary Reynolds number,Soret effect(initial solute concentration)and aspect ratio on the thermocapillary-buoyancy flow were emphatically analyzed.The results show that when the thermal capillary Reynolds number is small,the flow is axisymmetric and steady.At a larger thermal capillary Reynolds number,a second rotating roll cell emerges in the primary roll cell,whose rotating direction is the same with the primary roll cell.The second rotating roll is strengthened by the increase of the thermal capillary Reynolds number.When the thermal capillary Reynolds number exceeds a certain threshold value,the basic flow evolves into the hydrothermal waves.After that,the flow orderly undergoes the single-periodic oscillation flow,quasi-periodic oscillation flow and chaos phenomena with the increase of the thermal capillary Reynolds number.Due to the Soret effect in the binary mixture,the solute concentration near the inner wall is larger than that near the outer wall.In addition,a solute concentration fluctuation which is similar to the temperature fluctuation is observed on the free surface.The critical thermal capillary Reynolds number for the incipience of the three-dimensional oscillatory flow in binary mixtures is smaller than that in pure fluids,and decreases with the increase of the aspect ratio and initial solute concentration.Thus,the Soret effect in binary mixtures facilitates the flow instability.(3)When the capillary ratio is-1,a series of simulation were conducted to study the thermal-solutal capillary-buoyancy flow of a binary mixture in an annular pool.The annular pool was filled with the silicon-germanium melt with an initial silicon mass fraction of 1.99%.The Prandtl number and the Lewis number of the silicon-germanium melt are 6.37×10-3 and 2197.8,respectively.The thermal diffusion ability of this binary mixture is greater than the mass diffusion ability.When the capillary ratio is-1,the thermal-solutal capillary-buoyancy flow of a binary mixture always occurs,even in a very shallow annular pool that the buoyancy effect is ignored.Four kinds of flow patterns are demonstrated depending on the thermal capillary Reynolds number and the aspect ratio of the annular pool,including the two-dimensional steady flow,petal-like pattern,rosebud-like pattern and spoke pattern.When the capillary ratio slightly deviates from-1,the flow patterns do not have any structural change,while the characteristics of these flow patterns change slightly.A reverse transition from the unsteady petal-like pattern to the steady spoke pattern occurs in a very shallow annular pool where the aspect ratio is 0.05.(4)The thermal-solutal capillary-buoyancy flow of a binary mixture with a low Prandtl number in an annular pool with various aspect ratios and capillary ratios were performed by simulations.When the thermal capillary Reynolds number is relatively small,the thermal-solutal capillary-buoyancy flow is the basic flow.With the decrease of the capillary ratio,the evolution of flow pattern structure of this basic flow experiences three stages,the single counter-clockwise vortex,the combination of clockwise and counter-clockwise vortexes and the single clockwise vortex.The counter-clockwise and clockwise vortexes in the basic flow are respectively driven by thermal and solutal capillary effects.Besides the special case that the capillary ratio is-1,the basic flow is modulated by the spoke pattern with the increase of the thermal capillary Reynolds number.The critical thermal capillary Reynolds number for the incipience of the three-dimensional flow increases with the increases of the capillary ratio and decreases with increase of the aspect ratio of the annular pool.Seven kinds of three-dimensional flow patterns are observed in the annular pool,which are strongly dependent on the capillary ratio,thermal capillary Reynolds number and aspect ratio,including the petal-like pattern,spoke pattern,rosebud-like pattern,hydrosolutal waves,ear-like pattern,target-like pattern and copper coin-like pattern.With the decrease of capillary ratio and aspect ratio,the richness of flow pattern as well as the complexity of evolution will increase.