Dynamical Theory of Dendritic Growth in Convective Flow

Abstract

Preface. 1: Introduction. 1. Interfacial Pattern Formations in Dendritic Growth. 2. Dendritic Growth Interacting with Convective Flow. 3. Mathematical Formulation of the Problem. 2: Interfacial Wave Theory of Dendritic Growth with No Convection. 1. Steady State of Dendritic Growth with Zero Surface Tension Ivantsov's Solution. 2. The Basic State for Dendritic Growth with Nonzero Surface Tension. 3. Regular Perturbation Expansion of Axi-symmetric, Basic State of Dendritic Growth. 4. Global Interfacial Wave Instability. 5. Three-Dimensional, Linear Perturbed States around the Axi-symmetric Basic State of Dendritic Growth. 6. Outer Solution in the Outer Region away from the Singular Points. 7. The Inner Solutions near the Singular Point xic. 8. Tip Inner Solution to the Tip Region. 9. Global Trapped-Wave (GTW) Modes and Quantization Condition. 10. The Comparison of Theoretical Predictions with Experimental Data. 3: Steady Dendritic Growth from Melt with Convective Flow. 1. Mathematical Formulation of the Problem with Navier Stokes Model. 4: Steady Viscous Flow Past a Slender Paraboloid of Revolution. 1. Mathematical Formulation of the Problem. 2. The Oseen Model Problem. 3. Uniformly Valid Asymptotic Solution for Steady Viscous Flow Past a Slender Paraboloid of Revolution. 5: Asymptotic Solution of Dendritic Growth in External Flow (I). 1. Mathematical Formulation of the Problem. 2. Laguerre Series Representation of Solutions. 3.Asymptotic Expansion Form of the Solution as epsilon2--> 0. 6: Asymptotic Solution of Dendritic Growth in External Flow (II). 1. Laguerre Series Representation of Solutions. 2. Asymptotic Expansion Forms of the Solution for the Flow Field. 3. Leading-Order Asymptotic Solutions of Flow Field. 4. Asymptotic Expansion Solution of the Temperature Field. 5. A Brief Summary. 7: Steady Dendritic Growth with Natural Convection (I). 1. Mathematical Formulation of the Problem. 2. Laguerre Series Representation of Solutions. 3. Asymptotic Expansion Solution with Small Buoyancy Effect. 4. Summary. 8: Steady Dendritic Growth with Natural Convection (II). 1. Laguerre Series Representation and Asymptotic Forms of Solutions. 2. Leading Order Asymptotic Expansion Solutions. 3. First Order Asymptotic Expansion Solutions. 4. Summary of the Results. 9: Stability and Selection of Dendritic Growth with Convective Flow. 1. Basic Steady State Solution. 2. Linear Perturbed System around the Basic Steady State Solution. 3. Outer Expansion Solution. 4. Stability Criterion and Selection Condition of Tip Velocity. 5. Some Special Cases. 6. A Summary. 10: Concluding Remark. References.