On the basis of Xu’s interfacial wave theory, the stability of dendritic growth in a convective binary alloy melt with buoyancy effect is studied using the asymptotic method. The resulting asymptotic solution of equations reveals that the stability mechanism of dendritic growth in the binary alloy melt with buoyancy-driven convection is similar to that in a pure melt. Dendritic growth is stable above and unstable below a critical stability number 𝜀∗, which is determined by the quantization condition. In particular, there is a critical morphological number in the binary alloy melt. When the morphological number is less than the critical morphological number, the tip growth velocity increases, the tip curvature radius and oscillation frequency decrease, and the interface becomes thinner and smooth. When the morphological number is larger than the critical morphological number, the tip growth velocity decreases, the tip curvature radius and oscillation frequency increase, and the interface becomes fatter and rough. The result demonstrates that in a microgravity environment, there is a critical initial concentration such that below it thermal diffusion dominates, the tip growth velocity increases, the tip curvature radius and oscillation frequency decrease, and the interface becomes thinner and smooth; above it, solute diffusion dominates, the tip growth velocity decreases, the tip curvature radius and oscillation frequency increase, and the interface becomes fatter and rough.

中文翻译：

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具有浮力效应的二元合金熔体中枝晶生长的稳定性

以徐的界面波理论为基础，采用渐近方法研究了具有浮力效应的对流二元合金熔体中枝晶生长的稳定性。所得方程的渐近解表明，在具有浮力驱动的对流的二元合金熔体中枝晶生长的稳定性机制与纯熔体中的相似。枝晶生长在临界稳定数之上是稳定的，而在临界稳定值之下是不稳定的𝜀*，由量化条件决定。特别是，二元合金熔体中存在一个临界形态数。当形态数小于临界形态数时，尖端生长速度增加，尖端曲率半径和振荡频率减小，界面变薄光滑。当形态数大于临界形态数时，尖端生长速度降低，尖端曲率半径和振荡频率增加，界面变得更肥更粗糙。结果表明，在微重力环境中，存在一个临界初始浓度，在该浓度下，热扩散占主导地位，尖端生长速度增加，尖端曲率半径和振荡频率降低，界面变得更薄更光滑；在其之上，溶质扩散占主导地位，尖端生长速度减小，尖端曲率半径和振荡频率增加，界面变得更肥更粗糙。