Interfacial Fluid Dynamics and Transport Processes (Lecture Notes in Physics, 628)

✍ Scribed by Ranga Narayanan (editor), Dietrich Schwabe (editor)

• Publisher: Springer
• Year: 2003
• Tongue: English
• Leaves: 426
• Edition: 2003
• Category: Library

✦ Synopsis

Springer Verlag has been pleased to bring out this special volume on interfacial ?uid dynamics and transport processes. There are seventeen articles and each article is written in a pedagogical manner dealing with relevant research issues and questions. The intended audience is post-doctoral scientists, academicians and graduate students intending to pursue research and it is our hope that this volume will have lasting value. Several issues arise within the general ?eld of interfacial transport such as the instability of interfacial processes and driven ?ows. Instabilities occur when there is a sudden change in the structure of a solution as a control parameter is smoothly varied. They are usually accompanied by a change in the patterns in ?uid ?ow or temperature and concentration ?elds. Transport phenomena related instabilityattheinterfacehasmuchofitsoriginintheseminalworksofRayleigh whointhelaterpartofthe19thcenturyworkedonjets,gravitationallyunstably strati?ed ?uid layers, and on the ?rst ideas on convection. Some of these ideas were subsequently modi?ed by the work of Marangoni, Block and Pearson on surface tension driven instabilities. Over the years similar concepts have found place in solidi?cation and melting, electrodeposition, and other phase change problems.

✦ Table of Contents

front-matter
Chapter 1
Introduction
Physical and Mathematical Model
Numerical Method
Results and Discussion
Conclusions
Chapter 2
1 Introduction
2 Two-Fluid B´enard–Marangoni Instability
2.1 The Basic State of Conduction
2.2 The Governing Linearized Stability Equations and Boundary Conditions
2.3 Analysis and Results
3 Active Control of the Two-Fluid B´enard–Marangoni Instability
4 Discussion
Chapter 3
Introduction
The Lubrication Mechanism
Role of Vapor
The Force Balance Equation
Different Ways to Affect the Lubricating Film Shape
Mechanical and Electrostatic Rupture of the Interstitial Film
Heat Transmission across the Interfaces
Conclusions
Chapter 4
Introduction
Experimental Results
Linear Stability Analysis
Numerical Results
Conclusion and Outlook
Chapter 5
1 Introduction
2 Mechanisms of Convective Instabilities in a Single Layer
3 Mathematical Models
4 Two-Layer Systems
4.1 Marangoni Instabilities
4.2 Combined Rayleigh-Marangoni Convection
4.3 Anticonvection
4.4 In.uence of Lateral Walls
5 Three-Layer Systems
5.1 Combined Rayleigh-Marangoni Convection
5.2 Marangoni Convection in Systems with Deformable Interfaces
Chapter 6
1 Introduction
2 Experiments
2.1 Apparatus and Procedure
2.2 Experimental Results
3 Parallel Flow Model
4 Discussion
5 Conclusions
Chapter 7
1 Introduction
2 The Physics of Buoyancy and Interfacial- Gradient-Driven Convection in the Absence of Evaporation
2.1 Pure Rayleigh Convection or Buoyancy-Driven Convection
2.2 Pure Marangoni Convection or Interfacial Tension Gradient-Driven Convection
2.3 Physical E.ects of Multiple Fluid Layers
3 Physics of Evaporative Instability without Convection
4 The Physics of Evaporation with Convection
5 The Model
5.1 The Base State Solution and the Perturbed Equations
5.2 Results and Discussion
6 Scope for Future Work
Chapter 8
1 Introduction
1.1 Linear Stability Theory – Modal Approach
1.2 Generalized Linear Stability Theory
2 Autonomous Operator – Thermocapillary Spreading
2.1 Steady Traveling Wave Solutions
2.2 Linear Stability of Traveling Waves
2.3 Asymptotic Behavior
2.4 Optimal Ampli.cation Ratio
2.5 Pseudospectra
2.6 Optimal Perturbations – SVD
2.7 Summary of Thermocapillary Spreading Problem
3 Non-autonomous Operator: Marangoni Spreading from a Finite Surfactant Source
3.1 Surfactant Driven Flow
3.2 Base State Flow Pro.les
3.3 Linear Stability of Time Dependent Base State Pro.les
3.4 Transient Growth Analysis
3.5 Mechanism for Large Transient Growth
3.6 Summary of Marangoni Driven Spreading
4 Conclusion
Chapter 9
1 Introduction
2 Open Annulus Heated from the Outside Wall
2.1 Numerical Aspects
2.2 Results and Discussion
2.3 Conclusions
3 Liquid Bridge with a Curved Surface
3.1 Numerical Aspects
3.2 Results and Discussion
3.3 Conclusions
Appendix
Chapter 10
1 Introduction
2 Experimental Setup
3 Modes of Flow Instability
3.1 Phase Relationship of Temperature Oscillation
3.2 Non-contact Optical Pyrometry
3.3 Observation of Surface Oscillation by Phase-Shift Interferometry
4 E.ect of Oxygen Partial Pressure on the Surface-Tension-Driven Flow of Molten Silicon
4.1 Dependence of Surface Tension and Temperature Coe.cient on Oxygen Partial Pressure
4.2 Calibration of Oxygen Partial Pressure: Real Surface Tension at the Melt Surface
4.3 Oxygen Partial Pressure Dependence of Surface-Tension-Driven Flow
4.4 E.ect of Oxygen Partial Pressure on Temperature Oscillation
5 Flat Surface of a Czochralski Melt
6 Perspective on Future Work
Chapter 11
1 Introduction
2 Theoretical Estimates
2.1 Basic Assumptions and Equations
2.2 Laminar Boundary Layer Flow
2.3 Turbulent Flow
3 Computational Model
3.1 Geometry and Boundary Conditions
3.2 Numerical Method
4 Results
4.1 Flow Patterns
4.2 Scaling Properties
5 Summary and Conclusions
Chapter 12
1 Introduction
2 A Few De.nitions
2.1 Surface Tension
2.2 Thermocapillary Convection
3 The Liquid Bridge Con.guration
3.1 General Features
3.2 The Vorticity Singularities
3.3 Singularities and Flows with Free Surface: A Shortcut through the Moving Contact Line Problem
3.4 How to Deal with the Singularity?
3.5 The Regularized Problem
4 The Numerical Method
4.1 A Time-Stepping Method for the Stable States
4.2 To Compute the Steady States, Stable or Not
4.3 The Continuation Curve
4.4 Bifurcations
5 Results
5.1 Regularized Flows with n = 1
5.2 Quantitative E.ects of Increasing n
5.3 Symmetry Breaking
5.4 Energetics of the Most Destabilizing Mode
6 Towards a Regular Model?
7 Conclusion
Chapter 13
1 Introduction
2 Problem Formulation
3 Steady State Solution
4 Bifurcation Analysis
4.1 Numerical Results
Chapter 14
1 Introduction
1.1 Thermocapillary Flow in Liquid Bridges
1.2 The Interfacial Boundary Conditions
1.3 The Half Zone
2 Mathematical Description and Solution Technique
2.1 Formulation of the Problem
2.2 Expansion for Small Capillary Numbers
2.3 Thermocapillary Flow in a Fixed Domain
2.4 Leading-Order Dynamic Surface Deformation
3 Static Deformations
3.1 Methods of Solution
3.2 Some E.ects at Low Prandtl Numbers
3.3 High Prandtl Numbers
4 Dynamic Deformations
4.1 Processes Contributing to the Dynamic Deformations
4.2 Two-Dimensional Steady Flow
4.3 Three-Dimensional Dynamic Deformations at the Critical Point
5 Conclusions
Chapter 15
1 Introduction
2 Experimental Set-Up
3 Numerical Model
4 Modelling of Heat Exchange on the Free Surface
5 Experimental Results
5.1 Stability Diagram
5.2 Existence of Mixed Modes
5.3 Variation of the Temperature of the Cold Rod
6 Conclusions
Chapter 16
1 Introduction
2 Problem Formulation and Analysis
2.1 Model De.nition
2.2 Lubrication Scaling
2.3 An Analysis Using Lubrication Theory
2.4 Small Capillary Number Limit
2.5 Droplet Momentum Balance
3 Numerical Method
4 Results
5 Discussion
6 Conclusions
Chapter 17
1 Introduction
2 Electrocapillarity
3 Leaky Dielectric Experiments
4 Experiments with Non-zero Surface Charge
4.1 Mercury–Nitric Acid Experiment
4.2 Tangential Electric Fields with Ionic Surfactants
4.3 Perpendicular Electric Fields with Ionic Surfactants
5 Conclusions
Chapter 18
1 Introduction
2 The Volume-of-Fluid Method: Try It and You’ll Savor the (Finite) Di.erence
2.1 The Equations of Motion
2.2 Temporal Discretization and Projection Method
2.3 Advection of the Interface
2.4 Results
3 That’s Incurable! (Unless You Devise a Sharp-Interface VOF Algorithm)
3.1 Calculation of Surface Tension Force from Finite Di.erences of the VOF Function
3.2 Calculation of Surface Tension Force with a Sharp-Interface Algorithm
Chapter 19
1 Mathematical Model of Emulsion Motion
1.1 Introduction
1.2 Governing Equations
1.3 One-Dimensional Motion
2 Stability of the Space-Uniform State
2.1 Small Perturbations of the Space-Uniform State
2.2 Analysis of Some Limiting Cases
3 Discontinuous Solutions
3.1 Conditions on the Surface of Discontinuity
3.2 Simplest Discontinuous Solution and Its Stability
4 Solidi.cation of Emulsion
4.1 Formulation of the Problem
4.2 Additional Assumptions
4.3 Solvability of the Problems and Some Special Solutions
4.4 On the Problem of Control the Composition by Temperature
5 Thermocapillary Drift of a Drop near the Surfaces of Phase Transition
5.1 Statement of a Problem and Method of Solution
5.2 Thermocapillary Drift of a Drop in a Nonuniform Flow
5.3 Determination of the Non-stationary Shape of the Melt-Solid Front
5.4 Velocity of a Drop in Thermocapillary Drift
6 Discussion and Conclusion
Chapter 20
1 Introduction
2 Formulation of the Problem
3 Evaporation from a Liquid Layer
3.1 Exact Solution
3.2 Numerical Results
4 A Solidi.cation Front
5 Conclusions