Numerical simulation of the flow field in shaped crystal growth process

The purpose of this study is to clarify the effect of hydrodynamics on the bubble generation and repartition in shaped sapphire. The influence of the Reynolds numbers (in the meniscus and in the capillary channel) and of the Marangoni number on the flow field was studied with the help of numerical simulation. The governing equations (of mass and momentum conservation) and also the geometrical and physical parameters have been nondimensionalised. A strong influence of the Reynolds numbers in the meniscus (Re-men) and in the capillary channel (Re-cap) have been established. The velocities in the liquid decrease when Re-men increases and the maximum velocity position moves from the left of the exit of the capillary channel to the axis of symmetry. This behaviour is independent of the Re-cap. A critical value of Re-men was found for which the maximum velocity remains constant. The surface tension variation, leading to Marangoni effect, strongly influences the flow field. For a meniscus height of 100 mum the apparition of a loop in the flow field due to the surface tension variation was observed for Marangoni numbers (Ma) greater than a critical value (similar to1.5). Till this value the velocities are comparable to the pulling rate except a small region close to the meniscus surface where velocities are vanishing. The dimensions of the region above mentioned is comparable to the meniscus height. In this region it is possible that the gas contained in the liquid or the micro-bubbles accumulate till they are incorporated into the crystal. The maximum velocity of the meniscus surface shows a linear variation with the Marangoni number. For a constant Marangoni number and for different Reynolds numbers in the meniscus it was observed that the velocities composing the loop increase with the increase of the meniscus height.