Interfacial convection in multilayer systems:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
Springer
2006
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | X, 306 S. graph. Darst. |
| ISBN: | 0387221948 9780387221946 |
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| 100 | 1 | |a Nepomnjaščij, Aleksandr Abovič |d 1950- |e Verfasser |0 (DE-588)1024591697 |4 aut | |
| 245 | 1 | 0 | |a Interfacial convection in multilayer systems |c A. Nepomnyashchy ; I. Simanovskii ; J. C. Legros |
| 264 | 1 | |a New York, NY [u.a.] |b Springer |c 2006 | |
| 300 | |a X, 306 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Fluid dynamics | |
| 650 | 4 | |a Heat |x Convection | |
| 650 | 4 | |a Interfaces (Physical sciences) |x Mathematics | |
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| 700 | 1 | |a Simanovskij, Ilya B. |e Verfasser |4 aut | |
| 700 | 1 | |a Legros, Jean Claude |e Verfasser |4 aut | |
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Record in the Search Index
| _version_ | 1804135278658453504 |
|---|---|
| adam_text | Contents
Preface
.
v
1
Introduction
................................................... 1
1.1
Motivation
of the Problem
.................................... 1
1.2
Mathematical Models
........................................ 2
1.2.1
Sharp-Interface Approach
................................ 2
1.2.2
One-Layer Model
...................................... 4
1.2.3
Two-Layer Model
...................................... 10
1.2.4
Three-layer Model
...................................... 14
2
Types of Convective Instability in Systems with an Interface
........ 16
2.1
The Problem of Stability
...................................... 16
2.2
Rayleigh-Bénard
Convection
.................................. 18
2.2.1
Linear Stability
........................................ 18
2.2.2
Nonlinear Flow Regimes
................................ 23
2.3
Anticonvection
.............................................. 33
2.4
Stationary
Marangoni
Patterns
................................. 36
2.4.1
Exact Formulas
........................................ 36
2.4.2
Short-Wave
Marangoni
Patterns
........................... 37
2.4.3
Long-Wave
Marangoni
Patterns; The Case of Poorly
Conducting Boundaries
................................. 41
2.4.4
Long-Wave Deformational Instability
..................... 42
2.5
Marangoni
Waves in Systems with a Nondeformable Interface
...... 45
2.5.1
Oscillatory
Marangoni
Instability
......................... 45
2.5.2
Competition between
Marangoni
and Rayleigh Instability
Mechanisms
........................................... 52
2.5.3
Mode Mixing of
Interfacial
and Internal Waves
.............. 71
2.5.4
Oscillatory Instability in the Presence of a Thermal Gradient
and a Surfactant
........................................ 74
2.6
Marangoni
Waves in Systems with a Deformable Interface
......... 77
2.6.1
The Transverse
Marangoni
Instability in One-Layer Systems
.. 78
χ
Contents
2.6.2
The Limit of Large Ga and
M
............................ 80
2.6.3
Linear Theory of Transverse Instability: Numerical Results
.... 81
2.6.4
Nonlinear Theory of Transverse Instability
................. 84
2.6.5
Oscillations Generated by a Surfactant
..................... 90
2.6.6
Transverse and Longitudinal
Marangoni
Instabilities in the
Case of the Mass Transfer
................................ 96
3
Renard
Problem in Multilayer Systems with Undeformable
Interfaces
.....................................................100
3.1
General Equations and Boundary Conditions
.....................100
3.2
Linear Stability Theory
.......................................102
3.2.1
Marangoni
Convection. The Case of a Symmetric System and
Equal Layer Thicknesses
................................103
3.2.2
Onset of
Marangoni
Convection in Nonsymmetric
Three-Layer Systems
....................................108
3.2.3
Combined Action of
Marangoni
and Rayleigh Instability
Mechanisms
...........................................
Ill
3.3
Nonlinear Simulations
.......................................117
3.3.1
Marangoni
Convection. The Case of a Symmetric System
.....119
3.3.2
Marangoni
Convection. The Case of a Nonsymmetric System.
. 129
3.3.3
Rayleigh Convection
....................................141
3.3.4
Mixed Rayleigh-Marangoni Convection
....................148
3.3.5
Anticonvection
.........................................150
3.4
Space Experiments
..........................................152
3.4.1
Experiment Description
.................................152
3.4.2
Experiment 1
...........................................155
3.4.3
Experiment II
..........................................160
4
Bénard
Problem in Multilayer Systems with Deformable
Interfaces
.....................................................164
4.1
Formulation of the Problem
...................................164
4.2
Linear Stability Analysis
.....................................165
4.2.1
Long-Wave Asymptotics
.................................167
4.2.2
Neutral Stability Curves
.................................171
4.3
Nonlinear Theory
...........................................175
4.3.1
Derivation of the Amplitude Equations
.....................175
4.3.2
Traveling Wave Solutions
................................183
4.3.3
Results of Numerical Simulations
.........................189
5
Stability of Flows
...............................................194
5.1
Mechanisms of Instabilities
...................................194
5.1.1
Purely Thermocapillary Flows
............................194
5.1.2
Flows Under Combined Action of Thermocapillarity and
Buoyancy
.............................................196
5.2
Thermocapillary Flows in Two-Layer Systems
...................197
Contents xi
5.2.1 Basic
Equations
and Boundary Conditions
..................197
5.2.2
Stationary Flow Profiles
.................................199
5.2.3
Linear Stability Theory
..................................201
5.2.4
Nonlinear Patterns
......................................208
5.3
Buoyancy-thermocapillary Convection in Two-layer Systems
.......214
5.4
Buoyancy-thermocapillary Convection in Three-layer Systems
......222
5.4.1
Formulation of the Problem
..............................222
5.4.2
Results of Numerical Simulations
.........................225
5.5
Deformational Instabilities of Thermocapillary Flows in
Three-Layer Systems
........................................229
5.5.1
Formulation of the Model
................................232
5.5.2
Derivation of the Interface Evolution Equations
.............235
5.5.3
Linear Stability Analysis
.................................236
5.5.4
Weakly Nonlinear Model
................................240
6
Flows in Ultra-Thin Films
.......................................242
6.1
Lubrication Approximation
...................................242
6.2
Intermolecular Forces
........................................243
6.3
Generalized Cahn-Hilliard Equation
............................246
6.3.1
Model Formulation
.....................................246
6.3.2
Film Rupture
..........................................246
6.3.3
Film on an Inclined Plane
................................248
6.3.4
Two-Layer Films
.......................................248
6.3.5
Evaporating Films
......................................251
6.4
Diffuse-Interface Models
.....................................252
7
Outlook
.......................................................255
7.1
Extension of the Linear Stability Theory. Influence
of Lateral Boundaries
........................................255
7.2
Three-Dimensional Convective Flows
..........................257
7.3
Deformation of the Interface
..................................258
7.4
Transition to Chaos and
Interfacial
Turbulence
...................259
7.5
Multicomponent Fluids
.......................................260
7.6
Chemical Reactions
..........................................262
7.7
Porous Layers
..............................................263
7.8
Contact Line Dynamics
......................................265
7.9
Feedback Control of
Interfacial
Instabilities
......................266
7.10Biological Surface-Tension-Driven Flows
.......................270
References
.......................................................273
Index
...........................................................303
NEPOMNYASHCHY
·
SIMANOVSKII
·
LEGROS
Interfacial
Convection in Multilayer Systems
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.
|
| adam_txt |
Contents
Preface
.
v
1
Introduction
. 1
1.1
Motivation
of the Problem
. 1
1.2
Mathematical Models
. 2
1.2.1
Sharp-Interface Approach
. 2
1.2.2
One-Layer Model
. 4
1.2.3
Two-Layer Model
. 10
1.2.4
Three-layer Model
. 14
2
Types of Convective Instability in Systems with an Interface
. 16
2.1
The Problem of Stability
. 16
2.2
Rayleigh-Bénard
Convection
. 18
2.2.1
Linear Stability
. 18
2.2.2
Nonlinear Flow Regimes
. 23
2.3
Anticonvection
. 33
2.4
Stationary
Marangoni
Patterns
. 36
2.4.1
Exact Formulas
. 36
2.4.2
Short-Wave
Marangoni
Patterns
. 37
2.4.3
Long-Wave
Marangoni
Patterns; The Case of Poorly
Conducting Boundaries
. 41
2.4.4
Long-Wave Deformational Instability
. 42
2.5
Marangoni
Waves in Systems with a Nondeformable Interface
. 45
2.5.1
Oscillatory
Marangoni
Instability
. 45
2.5.2
Competition between
Marangoni
and Rayleigh Instability
Mechanisms
. 52
2.5.3
Mode Mixing of
Interfacial
and Internal Waves
. 71
2.5.4
Oscillatory Instability in the Presence of a Thermal Gradient
and a Surfactant
. 74
2.6
Marangoni
Waves in Systems with a Deformable Interface
. 77
2.6.1
The Transverse
Marangoni
Instability in One-Layer Systems
. 78
χ
Contents
2.6.2
The Limit of Large Ga and
M
. 80
2.6.3
Linear Theory of Transverse Instability: Numerical Results
. 81
2.6.4
Nonlinear Theory of Transverse Instability
. 84
2.6.5
Oscillations Generated by a Surfactant
. 90
2.6.6
Transverse and Longitudinal
Marangoni
Instabilities in the
Case of the Mass Transfer
. 96
3
Renard
Problem in Multilayer Systems with Undeformable
Interfaces
.100
3.1
General Equations and Boundary Conditions
.100
3.2
Linear Stability Theory
.102
3.2.1
Marangoni
Convection. The Case of a Symmetric System and
Equal Layer Thicknesses
.103
3.2.2
Onset of
Marangoni
Convection in Nonsymmetric
Three-Layer Systems
.108
3.2.3
Combined Action of
Marangoni
and Rayleigh Instability
Mechanisms
.
Ill
3.3
Nonlinear Simulations
.117
3.3.1
Marangoni
Convection. The Case of a Symmetric System
.119
3.3.2
Marangoni
Convection. The Case of a Nonsymmetric System.
. 129
3.3.3
Rayleigh Convection
.141
3.3.4
Mixed Rayleigh-Marangoni Convection
.148
3.3.5
Anticonvection
.150
3.4
Space Experiments
.152
3.4.1
Experiment Description
.152
3.4.2
Experiment 1
.155
3.4.3
Experiment II
.160
4
Bénard
Problem in Multilayer Systems with Deformable
Interfaces
.164
4.1
Formulation of the Problem
.164
4.2
Linear Stability Analysis
.165
4.2.1
Long-Wave Asymptotics
.167
4.2.2
Neutral Stability Curves
.171
4.3
Nonlinear Theory
.175
4.3.1
Derivation of the Amplitude Equations
.175
4.3.2
Traveling Wave Solutions
.183
4.3.3
Results of Numerical Simulations
.189
5
Stability of Flows
.194
5.1
Mechanisms of Instabilities
.194
5.1.1
Purely Thermocapillary Flows
.194
5.1.2
Flows Under Combined Action of Thermocapillarity and
Buoyancy
.196
5.2
Thermocapillary Flows in Two-Layer Systems
.197
Contents xi
5.2.1 Basic
Equations
and Boundary Conditions
.197
5.2.2
Stationary Flow Profiles
.199
5.2.3
Linear Stability Theory
.201
5.2.4
Nonlinear Patterns
.208
5.3
Buoyancy-thermocapillary Convection in Two-layer Systems
.214
5.4
Buoyancy-thermocapillary Convection in Three-layer Systems
.222
5.4.1
Formulation of the Problem
.222
5.4.2
Results of Numerical Simulations
.225
5.5
Deformational Instabilities of Thermocapillary Flows in
Three-Layer Systems
.229
5.5.1
Formulation of the Model
.232
5.5.2
Derivation of the Interface Evolution Equations
.235
5.5.3
Linear Stability Analysis
.236
5.5.4
Weakly Nonlinear Model
.240
6
Flows in Ultra-Thin Films
.242
6.1
Lubrication Approximation
.242
6.2
Intermolecular Forces
.243
6.3
Generalized Cahn-Hilliard Equation
.246
6.3.1
Model Formulation
.246
6.3.2
Film Rupture
.246
6.3.3
Film on an Inclined Plane
.248
6.3.4
Two-Layer Films
.248
6.3.5
Evaporating Films
.251
6.4
Diffuse-Interface Models
.252
7
Outlook
.255
7.1
Extension of the Linear Stability Theory. Influence
of Lateral Boundaries
.255
7.2
Three-Dimensional Convective Flows
.257
7.3
Deformation of the Interface
.258
7.4
Transition to Chaos and
Interfacial
Turbulence
.259
7.5
Multicomponent Fluids
.260
7.6
Chemical Reactions
.262
7.7
Porous Layers
.263
7.8
Contact Line Dynamics
.265
7.9
Feedback Control of
Interfacial
Instabilities
.266
7.10Biological Surface-Tension-Driven Flows
.270
References
.273
Index
.303
NEPOMNYASHCHY
·
SIMANOVSKII
·
LEGROS
Interfacial
Convection in Multilayer Systems
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. |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Nepomnjaščij, Aleksandr Abovič 1950- Simanovskij, Ilya B. Legros, Jean Claude |
| author_GND | (DE-588)1024591697 |
| author_facet | Nepomnjaščij, Aleksandr Abovič 1950- Simanovskij, Ilya B. Legros, Jean Claude |
| author_role | aut aut aut |
| author_sort | Nepomnjaščij, Aleksandr Abovič 1950- |
| author_variant | a a n aa aan i b s ib ibs j c l jc jcl |
| building | Verbundindex |
| bvnumber | BV021531828 |
| callnumber-first | Q - Science |
| callnumber-label | QC327 |
| callnumber-raw | QC327 |
| callnumber-search | QC327 |
| callnumber-sort | QC 3327 |
| callnumber-subject | QC - Physics |
| classification_rvk | SK 950 UP 7590 |
| ctrlnum | (OCoLC)249629973 (DE-599)BVBBV021531828 |
| dewey-full | 536.25 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 536 - Heat |
| dewey-raw | 536.25 |
| dewey-search | 536.25 |
| dewey-sort | 3536.25 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik Technik allgemein |
| discipline_str_mv | Physik Mathematik Technik allgemein |
| format | Book |
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| id | DE-604.BV021531828 |
| illustrated | Illustrated |
| index_date | 2024-07-02T14:25:35Z |
| indexdate | 2024-07-09T20:37:58Z |
| institution | BVB |
| isbn | 0387221948 9780387221946 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014748166 |
| oclc_num | 249629973 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-703 DE-11 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-703 DE-11 DE-188 |
| physical | X, 306 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Springer |
| record_format | marc |
| spelling | Nepomnjaščij, Aleksandr Abovič 1950- Verfasser (DE-588)1024591697 aut Interfacial convection in multilayer systems A. Nepomnyashchy ; I. Simanovskii ; J. C. Legros New York, NY [u.a.] Springer 2006 X, 306 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematik Fluid dynamics Heat Convection Interfaces (Physical sciences) Mathematics Marangoni effect Mehrschichtsystem (DE-588)4244347-7 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Grenzfläche (DE-588)4021991-4 gnd rswk-swf Hydrodynamik (DE-588)4026302-2 gnd rswk-swf Grenzflächenreaktion (DE-588)4308124-1 gnd rswk-swf Konvektion (DE-588)4117572-4 gnd rswk-swf Mehrschichtsystem (DE-588)4244347-7 s Grenzfläche (DE-588)4021991-4 s Konvektion (DE-588)4117572-4 s DE-604 Hydrodynamik (DE-588)4026302-2 s Grenzflächenreaktion (DE-588)4308124-1 s Mathematisches Modell (DE-588)4114528-8 s 1\p DE-604 Simanovskij, Ilya B. Verfasser aut Legros, Jean Claude Verfasser aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014748166&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014748166&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Nepomnjaščij, Aleksandr Abovič 1950- Simanovskij, Ilya B. Legros, Jean Claude Interfacial convection in multilayer systems Mathematik Fluid dynamics Heat Convection Interfaces (Physical sciences) Mathematics Marangoni effect Mehrschichtsystem (DE-588)4244347-7 gnd Mathematisches Modell (DE-588)4114528-8 gnd Grenzfläche (DE-588)4021991-4 gnd Hydrodynamik (DE-588)4026302-2 gnd Grenzflächenreaktion (DE-588)4308124-1 gnd Konvektion (DE-588)4117572-4 gnd |
| subject_GND | (DE-588)4244347-7 (DE-588)4114528-8 (DE-588)4021991-4 (DE-588)4026302-2 (DE-588)4308124-1 (DE-588)4117572-4 |
| title | Interfacial convection in multilayer systems |
| title_auth | Interfacial convection in multilayer systems |
| title_exact_search | Interfacial convection in multilayer systems |
| title_exact_search_txtP | Interfacial convection in multilayer systems |
| title_full | Interfacial convection in multilayer systems A. Nepomnyashchy ; I. Simanovskii ; J. C. Legros |
| title_fullStr | Interfacial convection in multilayer systems A. Nepomnyashchy ; I. Simanovskii ; J. C. Legros |
| title_full_unstemmed | Interfacial convection in multilayer systems A. Nepomnyashchy ; I. Simanovskii ; J. C. Legros |
| title_short | Interfacial convection in multilayer systems |
| title_sort | interfacial convection in multilayer systems |
| topic | Mathematik Fluid dynamics Heat Convection Interfaces (Physical sciences) Mathematics Marangoni effect Mehrschichtsystem (DE-588)4244347-7 gnd Mathematisches Modell (DE-588)4114528-8 gnd Grenzfläche (DE-588)4021991-4 gnd Hydrodynamik (DE-588)4026302-2 gnd Grenzflächenreaktion (DE-588)4308124-1 gnd Konvektion (DE-588)4117572-4 gnd |
| topic_facet | Mathematik Fluid dynamics Heat Convection Interfaces (Physical sciences) Mathematics Marangoni effect Mehrschichtsystem Mathematisches Modell Grenzfläche Hydrodynamik Grenzflächenreaktion Konvektion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014748166&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014748166&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT nepomnjascijaleksandrabovic interfacialconvectioninmultilayersystems AT simanovskijilyab interfacialconvectioninmultilayersystems AT legrosjeanclaude interfacialconvectioninmultilayersystems |