Interfacial Wave Theory of Pattern Formation: Selection of Dendritic Growth and Viscous Fingering in Hele-Shaw Flow

摘要: 1. Introduction.- 1.1 Interfacial Pattern Formations in Dendrite Growth and Hele-Shaw Flow.- 1.2 A Brief Review of the Theories Free Growth.- 1.2.1 Maximum Velocity Principle (1976).- 1.2.2 Marginal Stability Hypothesis (1978).- 1.2.3 Microscopic Solvability Condition (MSC) Theory (1986-1990s).- 1.2.4 Wave (IFW) (1990).- 1.3 Macroscopic Continuum Model.- 1.3.1 Transport Equations.- 1.3.2 The Interface Conditions.- 1.3.3 Scaling Dimensionless System.- References.- 2. Unidirectional Solidification Mullins-Sekerka Instability.- 2.1 with Planar from a Pure Melt.- 2.1.1 Basic Steady State Solution.- 2.1.2 Unsteady Perturbed Solutions 2.1.3 Asymptotic Long-Wavelength Regime, k = O(?).- 2.1.4 Extremely Short-Wavelength O (1/ ?).- 2.2 Binary Mixture.- 2.2.1 Mathematical Formulation Problem.- 2.2.2 State.- 2.2.3 Solutions.- 2.2.4 2.2.5 O(1/ ?) g O1/ 2.2.6 Some Remarks on Solidification.- 3. 3.1 Three-Dimensional Axially Symmetric 3.2 Two-Dimensional Reference.- 4. Zero Surface Tension Its Regular Perturbation Expansion.- 4.1 Ivantsov Solution Unsolved Fundamental Problems..- 4.2 Needle 4.2.1 Formulation.- 4.2.2 Expansion (RPE) as ?? 0.- 4.2.3 Behavior ? -> ?.- 4.3 Two-Dimensional, Crystal 4.3.1 4.3.2 4.3.3 4.4 Summary Discussion.- 5. for Nonzero Tension.- 5.1 Nash-Glicksman Problem Classic 5.2 Geometric Model Formation 5.2.1 5.2.2 Segur-Kruskal 5.2.3 Nonclassic 5.2.4 5.3 Dendritic 5.3.1 Complete 6. Global Instability 6.1 Linear System Around 6.2 Outer Region away Tip.- 6.2.1 Zeroth-Order Approximation.- 6.2.2 First-Order 6.2.3 Singular Point ?cof 6.3 Inner near ?c.- 6.4 Tip Region.- 6.5 Trapped-Wave Modes Quantization Condition.- 6.6 6.7 Comparison Theoretical Predictions Experimental Data.- 7. Effect Anisotropy Low-Frequency 7.1 7.2 Multiple Variable 7.3 Equation 7.3.1 Case I: ?0= O(l).- 7.3.2 II: |?0| 1.- 7.3.3 Summary.- 7.4 Matching 7.5 Spectra Eigenvalues Mechanisms.- 7.5.1 7.5.2 7.6 7.7 Selection Conditions 8. Mixtures.- 8.1 8.2 8.3 8.4 MVE 8.4.1 8.4.2 8.5 8.6 8.7 Comparisons Results 9. Viscous Fingering Cell.- 9.1 9.2 9.3 Smooth Finger 9.4 General Curvilinear Coordinates (?,?)and 9.5 9.6 9.6.1 O(1).- 9.6.2 ?1.- 9.7 9.7.1 Spectrum Complex GTW 9.7.2 Real LF 9.8 Flow Nose Bubble.- 9.8.1 Bubble Perturbation.- 9.8.2 9.9 Criteria References.