A Strongly Coupled Analytical Study of the Interaction of Foreign Particles with a Solid-Liquid Interface in the Presence of Morphological and Fluid Instabilities

这个项目的目的是对生长中的晶体界面和不溶性球形外来粒子之间的相互作用进行分析研究。采用定向凝固装置研究了温度和浓度分布、颗粒运动引起的流体流动、对流、溶质偏析、界面变形和移动界面附近颗粒存在之间的耦合。该数学模型以能量、溶质、质量和动量守恒方程为基础，辅以一组适当的边界条件。得到的无维系统显示了几个无维分组，所有这些分组在随后的分析中都有作用。这将预测主要的晶体形态、界面形状的稳定性标准、对流和密度平流效应，并确定分离粒子推动和捕获的阈值参数值。将使用弱非线性分岔分析来确定理论预测是否可以通过实验验证。该方法需要使用微扰技术、渐近分析、双球坐标系、适合于弱非线性分析的分岔方法和一些数值方法。随着二十一世纪的临近，科学家和技术人员面临着越来越大的压力，以满足社会对低重量、高可靠性材料的需求。例如，在航空航天工业中，减轻重量有助于增加飞行中的有效载荷能力，节省运营成本，提高速度和更远的航程。然而，较轻的材料需要通过添加不同物质的微小颗粒来增强。这反过来又使制造过程复杂化。最终铸件应该使这些颗粒均匀分布，但实际上，这很难实现。缺陷是由于凝固过程中熔体中颗粒的迁移而产生的，并且对最终产品的质量有害。实验工作为如何克服这些困难提供了一些指示。鉴于大量的加工和物理变量，这些局部解无法清楚地将加工历史与铸件的组成联系起来。量化各种工艺参数对最终铸件的影响仍然是一项关键任务，这是我们分析工作的目的。

Hadji 9700380 The objective of this project is to conduct an analytical study of the interaction between a growing crystal interface and insoluble spherical foreign particles. A directional solidification set-up is considered to study the coupling between the distributions of temperature and concentrations, fluid flow due to particle movement, convection, solute segregation, interfacial deformations and particle presence near the moving interface. The mathematical model, based on the conservation equations of energy, solute, mass and momentum, is complemented by a set of appropriate boundary conditions. The resulting non-dimensional system displays several dimensionless groupings, all of which have a role in the subsequent analysis. This will predict the dominant crystal morphology, stability criteria for interface shape, convection and density advection effects and determine the threshold parameter values that separate pushing and capture of particles. A weakly nonlinear bifurcation analysis will be used to determine if the theoretical predictions can be verified experimentally. The methodology requires the use of perturbation techniques, asymptotic analysis, the bispherical coordinate system, bifurcation methods appropriate to weakly nonlinear analysis, and some numerical methods. As we approach the twenty-first century, scientists and technologists are under increasing pressures to satisfy society's need for materials of lower weight and higher reliability. For instance, in the aerospace industry, a reduced weight facilitates an increased payload capacity in flight, operating cost savings, higher speeds and longer range flights. However, lighter materials need to be strengthened by the addition of tiny particles of a different substance. This in turn complicates the manufacturing process. The final cast should have these particles uniformly distributed but, in practical terms, this is difficult to achieve. Imperfections arise due to the migration of the particles in the melt during the solidification process, and are detrimental to the quality of the end product. Some indications of how to overcome these difficulties have been provided by experimental work. In view of the large number of processing and physical variables, these partial solutions are unable to clearly relate the processing history to the constitution of the cast. There remains the crucial task of quantifying the influence of the various processing parameters on the final cast, and this is the aim of our analytical work.