Onset of convection during vertical directional dendritic solidification and the stabilizing effect of the two-phase region

The onset of convection during vertical directional dendritic solidification has been examined experimentally and numerically. The effects of the two-phase region are significant in determining the breakdown of the buoyantly unstable solutal diffusion layer produced during solidification of an NH₄CI-H₂O solution. The transition to convection was experimentally characterized by a combined solutal and thermal Rayleigh number using interferometry. The critical combined Rayleigh number is dependent on the two-phase effects of the dendritic mushy zone. A linear stability model used measured values for effective primary dendrite arm spacings to model the experiments and yielded the same exponential dependence for critical combined Rayleigh number versus two-phase region height. The model includes an allowance for shrinkage flow and two-phase inertial effects. These terms have a significant influence on breakdown at high growth rates. The two-phase effects were characterized by the height of the mushy zone. The critical combined Rayleigh number is an exponential function of this distance. Application of the model to the eutectic growth of NH₄CI-H₂O show that growth is stable for reduced levels of gravity and also for high growth rates.