Dynamical theory of dendritic growth in convective flow /
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Author / Creator: | Xu, Jian-Jun, 1940- |
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Imprint: | Boston : Kluwer Academic, c2004. |
Description: | xii, 240 p. : ill. ; 25 cm. |
Language: | English |
Series: | Advances in mechanics and mathematics ; v. 7 |
Subject: | Crystalline interfaces. Solid-liquid interfaces. Liquid-liquid interfaces. Dendritic crystals. Crystal growth. Fluid dynamics. Pattern formation (Physical sciences) Crystal growth. Crystalline interfaces. Dendritic crystals. Fluid dynamics. Liquid-liquid interfaces. Pattern formation (Physical sciences) Solid-liquid interfaces. |
Format: | Print Book |
URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/5172017 |
Table of Contents:
- Preface
- 1.. Introduction
- 1. Interfacial Pattern Formations in Dendritic Growth
- 2. Dendritic Growth Interacting with Convective Flow
- 3. Mathematical Formulation of the General Problem
- 3.1. Scaling
- 3.2. Macroscopic Transport Equations
- 3.3. Interface Conditions
- 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
- 3.1. O([epsilon superscript 0])
- 3.2. O([epsilon superscript 2])
- 3.3. The Asymptotic Behavior of the Regular Perturbation Expansion Solution as [xi] to [infinity]
- 3.4. Some Numerical Results of the Interface Shape Correction
- 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
- 6.1. Zeroth-Order Approximation
- 6.2. First-Order Approximation
- 6.3. Singular Point [xi subscript c] of the Outer Solution and Stokes Phenomenon
- 7. The Inner Solutions near the Singular Point [xi subscript c]
- 8. Tip Inner Solution in the Tip Region
- 9. Global Trapped-Wave (GTW) Modes and the Quantization Condition
- 10. The Comparison of Theoretical Predictions with Experimental Data
- 3.. Steady Dendritic Growth from Melt with Convective Flow
- 1. Mathematical Formulation of Problem with Navier-Stokes Model
- 4.. Steady Viscous Flow Past a Paraboloid of Revolution
- 1. Mathematical Formulation of the Problem
- 2. The Oseen Model Problem
- 2.1. Laguerre Series Representation of Solutions
- 2.2. Solution of the Oseen Model and the Paradox
- 2.3. The Solution of Type (I)
- 2.4. The Solution of Type (II)
- 2.5. The Paradox of Oseen Model Solutions and Its Resolution
- 2.6. Appendix (A)
- 2.6.1. The Properties of Laguerre Functions
- 2.6.2. Important Formulas
- 2.6.3. The derivation of the solution {{A[subscript n], B[subscript n]}} for (4.44)
- 2.6.4. The Determination of the Functions: {{A[subscript n,k]([tau]), A[subscript n,k]([tau]), B[subscript n,k]([tau]), B[subscript n,k]([tau])}}
- 3. Uniformly Valid Asymptotic Solution for Steady Viscous Flow past a Slender Paraboloid of Revolution
- 3.1. Mathematical Formulation of the Problem
- 3.2. Laguerre Series Representation of Solutions
- 3.3. Outer Asymptotic Expansion Solution in the Limit Re to 0
- 3.3.1. Zeroth-Order Solution of Velocity Field O(v[subscript 0]([epsilon subscript 0]))
- 3.4. Inner Asymptotic Expansion of the Solution
- 3.4.1. The Zeroth-Order Inner Solution
- 3.5. Matching Conditions of the Solutions
- 3.6. Skin Friction at the Surface of a Paraboloid
- 3.7. Appendix (B)
- 3.7.1. Asymptotic behavior of the outer solution [psi subscript 0] in the limit [tau] to 0
- 3.7.2. Determination of the special outer solution [psi]*[subscript 0]
- 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 [epsilon subscript 0] to 0
- 3.1. Leading-Order Solutions of Flow Field
- 3.2. Zeroth-Order Solution of Temperature Field O(1)
- 3.3. First Order Solution of Temperature Field O([epsilon subscript 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
- 2.1. Outer Expansion Form of the Solution
- 2.2. Inner Expansion Form of the Solution
- 3. Leading-Order Asymptotic Solutions of Flow Field
- 3.1. Zeroth-Order Outer Solution of the Velocity Field
- 3.2. First Sequence of Inner Solutions of the Velocity Field
- 3.3. Second Sequence of Inner Solutions of the Velocity Field
- 3.4. Matching Conditions for Leading-Order Solutions of the Flow Field
- 4. Asymptotic Expansion Solution of the Temperature Field
- 4.1. First Sequence of Solutions of the Temperature Field
- 4.2. Second Sequence of Solutions 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
- 3.1. Zeroth-Order Solution of the Temperature Field O(1)
- 3.2. Zeroth-Order Solution of the Velocity Field O([epsilon subscript 0])
- 3.3. First-Order Solution of the Temperature Field O([epsilon subscript 0])
- 4. Summary
- 8.. Steady Dendritic Growth with Natural Convection (II)
- 1. Laguerre Series Representation and Asymptotic Forms of Solutions
- 1.1. Laguerre Series Representation of the Solution
- 1.2. Outer Expansion Form of the Solution
- 1.3. Inner Expansion Form of the Solution
- 2. Leading-Order Asymptotic Expansion Solutions
- 2.1. Leading-Order Asymptotic Expansion Solution of the Temperature Field
- 2.2. Leading-Order Inner Solutions of the Velocity Field O([epsilon superscript 2 subscript 2])
- 2.3. Leading-Order Outer Solutions of the Velocity Field O(v[subscript 0]([epsilon subscript 2]))
- 2.4. Matching Conditions for the Leading Order Solutions of the Flow Field
- 3. First-Order Asymptotic Expansion Solutions
- 3.1. First-Order Asymptotic Solution for the Temperature Field
- 4. Summary of the Results
- 9.. Stability and Selection of Dendritic Growth with Convective Flow
- 1. Basic Steady State Solution
- 1.1. Convection Flow Field Induced by Uniform External Flow
- 1.2. Convection Flow Field Induced by Buoyancy Effect
- 1.3. Convection Motion Induced by Density Change During Phase Transition
- 1.4. More General Steady State Solutions with Nearly Paraboloid Interface
- 2. Linear Perturbed System around the Basic Steady State Solution
- 3. Outer Expansion Solution
- 3.1. Zeroth-Order Multiple Variables Expansion (MVE) Solutions
- 3.2. First-Order Approximation
- 4. Stability Criterion and Selection Condition of Tip Velocity
- 5. Some Special Cases
- 5.1. Convection Motion Induced by Uniform External Flow with Pr [double greater-than sign] 1
- 5.2. Convection Motion Induced by Buoyancy Effect with Pr [double greater-than sign] 1
- 5.3. Convection Motion Induced by Density Change During Phase Transition
- 6. A Summary
- 10.. Concluding Remark
- References