具有明确边界条件的多组元体系在凝固时, 溶液内的热量和质量输运方程的严格求解非常困难, 因此简化方程是十分必要的. 本文在普适流体力学方程的基础上, 采用表征流体特征的无量纲参数和适当的边界条件, 简化了扩散方程. 证实了简化后的质量扩散模型在凝固现象中的物理有效性. 指出由扩散引起的整体流的实质是微对流, 它环绕着固液界面流动, 并限制在质量边界层内, 即固液界面溶液一侧溶质浓度有显著变化的区域内. 我们的氧化物晶体生长实验结果已经证实了上述结论的正确性. 为了强调质量流的物理概念, 讨论采用了二维双组元模型.
Rigorous modeling of heat and mass transfer in multicomponent (solidification) fluid for realistic boundary conditions is typically unwieldy. Hence, the motivation for simplification
is great. In this presentation, based on the generally valid transport equations and the appropriate dimensionless groups of fluid properties,
we point out (a)physically justifiable applications of mass diffusional transfer models for solidified fluid, and (b)the diffusion-induced bulk
flow denoted as micro-convection, which flows around the solid-liquid interface inside the width δc of interfacial liquid zone of significant
concentration changes. Our laboratory practice for oxide crystal growth has given valuable evidence for these considerations. Since the emphasis
is on the express of concept, we limit the discussion mostly to two-dimensional models in a binary system.
参考文献
| [1] | Dikov M S. High Temp., 1999, 7: 150-152. [2] Maksimov Yu M, Kirdyashkin A I, Ziatdinov M Kh, et al. Fiz. Goreniya Vzryva, 2000, 36: 52-59 (Russian). [3] Mack T, Tensi H M, Z. Metallkd., 2000, 91: 397-400. [4] Jin W Q, Pan L Z, Cai L X, et al. J. Crystal Growth, 1999, 206: 81-87. [5] Jin W Q, Liang X A, Cai L X, et al. International J. of Modern Physics, 2002, 16: 122-127. [6] Jin W Q, Pan Z L, Liu Z H. J. Crystal Growth, 1998, 191: 760-766. |
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