This book contains a systematic investigation of the convection in systems with interfaces. For the first time, it classifies all of the known types of convective instabilities in such systems, and discusses the peculiarities of multilayer systems. The book provides an overview of the wide variety of steady and oscillatory patterns, waves, and other dynamic phenomena characteristic for multilayer fluid systems. Various physical effects, including heat and mass transfer, thermal and mechanical couplings on the interfaces, interfacial deformability, the influence of surfactants on different types of convective motions are investigated. The text will be useful for researchers and graduate students in fluid mechanics, nonlinear dynamics and applied mathematics as well as for physicists and chemical engineers interested in the investigation of the interfacial physico-chemical processes and in their applications.

Preface

v

Introduction

1

(15)

Motivation of the Problem

1

(1)

Mathematical Models

2

(14)

Sharp-Interface Approach

2

(2)

One-Layer Model

4

(6)

Two-Layer Model

10

(4)

Three-layer Model

14

(2)

Types of Convective Instability in Systems with an Interface

16

(84)

The Problem of Stability

16

(2)

Rayleigh-Benard Convection

18

(15)

Linear Stability

18

(5)

Nonlinear Flow Regimes

23

(10)

Anticonvection

33

(3)

Stationary Marangoni Patterns

36

(9)

Exact Formulas

36

(1)

Short-Wave Marangoni Patterns

37

(4)

Long-Wave Marangoni Patterns; The Case of Poorly Conducting Boundaries

41

(1)

Long-Wave Deformational Instability

42

(3)

Marangoni Waves in Systems with a Nondeformable Interface

45

(32)

Oscillatory Marangoni Instability

45

(7)

Competition between Marangoni and Rayleigh Instability Mechanisms

52

(19)

Mode Mixing of Interfacial and Internal Waves

71

(3)

Oscillatory Instability in the Presence of a Thermal Gradient and a Surfactant

74

(3)

Marangoni Waves in Systems with a Deformable Interface

77

(23)

The Transverse Marangoni Instability in One-Layer Systems

78

(2)

The Limit of Large Ga and M

80

(1)

Linear Theory of Transverse Instability: Numerical Results

81

(3)

Nonlinear Theory of Transverse Instability

84

(6)

Oscillations Generated by a Surfactant

90

(6)

Transverse and Longitudinal Marangoni Instabilities in the Case of the Mass Transfer

96

(4)

Benard Problem in Multilayer Systems with Undeformable Interfaces

100

(64)

General Equations and Boundary Conditions

100

(2)

Linear Stability Theory

102

(15)

Marangoni Convection. The Case of a Symmetric System and Equal Layer Thicknesses

103

(5)

Onset of Marangoni Convection in Nonsymmetric Three-Layer Systems

108

(3)

Combined Action of Marangoni and Rayleigh Instability Mechanisms

111

(6)

Nonlinear Simulations

117

(35)

Marangoni Convection. The Case of a Symmetric System

119

(10)

Marangoni Convection. The Case of a Nonsymmetric System

129

(12)

Rayleigh Convection

141

(7)

Mixed Rayleigh-Marangoni Convection

148

(2)

Anticonvection

150

(2)

Space Experiments

152

(12)

Experiment Description

152

(3)

Experiment I

155

(5)

Experiment II

160

(4)

Benard Problem in Multilayer Systems with Deformable Interfaces

164

(30)

Formulation of the Problem

164

(1)

Linear Stability Analysis

165

(10)

Long-Wave Asymptotics

167

(4)

Neutral Stability Curves

171

(4)

Nonlinear Theory

175

(19)

Derivation of the Amplitude Equations

175

(8)

Traveling Wave Solutions

183

(6)

Results of Numerical Simulations

189

(5)

Stability of Flows

194

(48)

Mechanisms of Instabilities

194

(3)

Purely Thermocapillary Flows

194

(2)

Flows Under Combined Action of Thermocapillarity and Buoyancy

196

(1)

Thermocapillary Flows in Two-Layer Systems

197

(17)

Basic Equations and Boundary Conditions

197

(2)

Stationary Flow Profiles

199

(2)

Linear Stability Theory

201

(7)

Nonlinear Patterns

208

(6)

Buoyancy-thermocapillary Convection in Two-layer Systems

214

(8)

Buoyancy-thermocapillary Convection in Three-layer Systems

222

(7)

Formulation of the Problem

222

(3)

Results of Numerical Simulations

225

(4)

Deformational Instabilities of Thermocapillary Flows in Three-Layer Systems

229

(13)

Formulation of the Model

232

(3)

Derivation of the Interface Evolution Equations

235

(1)

Linear Stability Analysis

236

(4)

Weakly Nonlinear Model

240

(2)

Flows in Ultra-Thin Films

242

(13)

Lubrication Approximation

242

(1)

Intermolecular Forces

243

(3)

Generalized Cahn-Hilliard Equation

246

(6)

Model Formulation

246

(1)

Film Rupture

246

(2)

Film on an Inclined Plane

248

(1)

Two-Layer Films

248

(3)

Evaporating Films

251

(1)

Diffuse-Interface Models

252

(3)

Outlook

255

(18)

Extension of the Linear Stability Theory. Influence of Lateral Boundaries

255

(2)

Three-Dimensional Convective Flows

257

(1)

Deformation of the Interface

258

(1)

Transition to Chaos and Interfacial Turbulence

259

(1)

Multicomponent Fluids

260

(2)

Chemical Reactions

262

(1)

Porous Layers

263

(2)

Contact Line Dynamics

265

(1)

Feedback Control of Interfacial Instabilities

266

(4)

Biological Surface-Tension-Driven Flows

270

(3)

References

273

(30)

Index

303

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Interfacial Convection in Multilayer Systems

9780387221946

0387221948

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