Interfacial Wave Theory of Pattern Formation Selection of Dendritic Growth and Viscous Fingering in Hele-Shaw Flow
The stabiltiy mechanisms of a curved front and the pattern formation in dendrite growth and viscous fingering have been fundamental subjects in the areas of condensed-matter physics, materials science, crystal growth, and fluid mechanics for about half a century. This book studies interfacial instab...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
1998, 1998
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| Edition: | 1st ed. 1998 |
| Series: | Springer Series in Synergetics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 7.5 The Spectra of Eigenvalues and Instability Mechanisms
- 7.6 Low-Frequency Instability for Axially Symmetric Dendrite Growth
- 7.7 The Selection Conditions for Dendrite Growth
- References
- 8. Three-Dimensional Dendrite Growth from Binary Mixtures
- 8.1 Mathematical Formulation of the Problem
- 8.2 Basic State Solution for the Case of Zero Surface Tension
- 8.3 Linear Perturbed System for the Case of Nonzero Surface Tension
- 8.4 The MVE Solutions in the Outer Region
- 8.5 The Inner Solutions near the Singular Point ?c
- 8.6 Global Modes and the Quantization Condition
- 8.7 Comparisons of Theoretical Results with Experimental Data
- 9. Viscous Fingering in a Hele-Shaw Cell
- 9.1 Introduction
- 9.2 Mathematical Formulation of the Problem
- 9.3 The Smooth Finger Solution with Zero Surface Tension
- 9.4 Formulation of the General Problem in Curvilinear Coordinates (?,?)and the Basic State Solutions
- 9.5 The Linear Perturbed System and the Outer Solutions
- 9.6 The Inner Equation near the Singular Point ?c
- 9.7 Eigenvalues Spectra and Instability Mechanisms
- 9.8 Fingering Flow with a Nose Bubble
- 9.9 The Selection Criteria of Finger Solutions
- 5.2 The Geometric Model and Solutions of the Needle Crystal Formation Problem
- 5.3 The Nonclassic Steady State of Dendritic Growth with Nonzero Surface Tension
- 6. Global Interfacial Wave Instability of Dendrite Growth from a Pure Melt
- 6.1 Linear Perturbed System Around the Basic State of Three-Dimensional Dendrite Growth
- 6.2 Outer Solution in the Outer Region away from the Tip
- 6.3 The Inner Solutions near the Singular Point ?c
- 6.4 Tip Inner Solution in the Tip Region
- 6.5 Global Trapped-Wave Modes and the Quantization Condition
- 6.6 Global Interfacial Wave Instability of Two-Dimensional Dendrite Growth
- 6.7 The Comparison of Theoretical Predictions with Experimental Data
- 7. The Effect of Surface Tension Anisotropy and Low-Frequency Instability on Dendrite Growth
- 7.1 Linear Perturbed System Around the Basic State.-7.2 Multiple Variable Expansion Solution in the Outer Region
- 7.3 The Inner Equation near the Singular Point ?c
- 7.4 Matching Conditions
- 1. Introduction
- 1.1 Interfacial Pattern Formations in Dendrite Growth and Hele-Shaw Flow
- 1.2 A Brief Review of the Theories of Free Dendrite Growth
- 1.3 Macroscopic Continuum Model
- 2. Unidirectional Solidification and the Mullins-Sekerka Instability
- 2.1 Solidification with Planar Interface from a Pure Melt
- 2.2 Unidirectional Solidification from a Binary Mixture
- 3. Mathematical Formulation of Free Dendrite Growth from a Pure Melt
- 3.1 Three-Dimensional Axially Symmetric Free Dendrite Growth
- 3.2 Two-Dimensional Free Dendrite Growth
- 4. Steady State of Dendrite Growth with Zero Surface Tension and Its Regular Perturbation Expansion
- 4.1 The Ivantsov Solution and Unsolved Fundamental Problems.
- 4.2 Three-Dimensional Axially Symmetric Steady Needle Growth
- 4.4 Summary and Discussion
- 5. The Steady State for Dendrite Growth with Nonzero Surface Tension
- 5.1 The Nash-Glicksman Problem and the Classic Needle Crystal Solution