Recent developments of the numerical simulations of three dimensional Marangoni convection were reviewed. Based on the authors recent results of numerical simulations conducted by using a finite difference method, general feature of oscillatory Marangoni convection in half-zone liquid bridges of low Prandtl number fluids ( Pr= 0 , 0.01, 0.02) with a cylindrical liquid surface was discussed over a wide range of aspect ratio (As=0.6 to 2.2) . The simulation results indicated that under smaller temperature differences the flow in the liquid bridge was axisymmetric , but the flow became steady 3-D at and beyond the first critical Reynolds number Rec1. This steady 3-D flow became unstable against time-de pendent 3-D disturbances beyond a second critical condition, Re, 2. The numerical simulations revealed the critical conditions and flow structures in detail for Pr=0 fluid and rough sketches for fluids of Pr=0.01 and 0.02. These non-linear simulations gave reasonable values of Rec1 in good agreements with those of linear stability analyses and also Re,2 close to the available numerical results. A stability map for low Pr fluids ( Pr=0, 0.01 and 0.02) indicates the effect of aspect ratio on the critical Reynolds numbers.
Transition behavior from steady to oscillatory thermocapillary flow was experimentally studied in a liquid bridge of molten tin under normal gravity. The experimental difficulties such as preventing oxidation of the melt surface and detecting small amplitude of surface temperature fluctuation were successfully solved. The transition was detected by temperature fluctuation measurement of the melt surface and directly proved by a surface flow visualization experiment in which tin-oxide particles pre-mixed with the melt were used as the tracer. Those results are the first experimental evidence for the transition to oscillatory flow in a low Prandtl fluid, which has never observed yet. Significance of a microgravity experiment is quantitatively shown also.
Research on Marangoni convection in a silicon melt for a low Prandtl number fluid is reviewed. Temperature
measurement and flow visualization in a half-zone bridge of molten silicon were carried out under microgravity conditions us ing the NASDA TR-IA rocket and on the ground. Formation ofnon-axisymmetric temperature field due to the Maran goni flow instability was revealed. The effect of oxygen partial pressure on Marangoni convection was also investigated. A transition from non-periodic fluctuations to periodic fluctuations was observed when oxygen partial pressure was increased. This result indicates that oxygen partial pressure in the ambient atmosphere plays an important role in the Marangoni flow stability of molten silicon. The non-contact temperature measurement by a Si-CCD device and the phase shift laser interferometry would be effective tools to study Marangoni convection of molten silicon bridge.
Surface tension of silicon melt was measured with the sessile drop method under precisely controlling the oxygen partial pressure, Po2, in argon atmosphere in relation to Po2, and temperature . Obtained dependences of the surface tension and its temperature coefficient on Po2, in the range of Po2, Po2,sat were fairly well described with Szyskowski's equation and also the equations of temperature coefficient which were derived by authors . Results obtained under Po2, Po2,sat may have a close relation to the surface tension behavior of silicon melt in the Czochralski process. Deep understanding and explanation of the results obtained under Po2, Po2, sat are still remained for the task of a future study.
In order to confirm the effect of the micro-gravity on the distribution of impurity in the space grown crystal, Te doped GaSb single crystal was re-grown by vertical gradient freeze method (VGF) under terrestrial condition. Te con centration distribution in the re-grown GaSb crystal was measured by spatially resolved photoluminescence (SRPL) and it was found that the concentration profile was rather close to the calculation based on the complete mixing model. The cross section was investigated after striation etching and it was found that clear impurity striations appeared in the later part of the crystal. In contrast to the previous space experiment where Marangoni convection as well as the thermal convection were eliminated, it was confirmed that strong buoyancy driven convection was found to exist in the melt during the growth experiment under terrestrial condition.