Mechanical and thermodynamical modeling of fluid interfaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
2001
|
| Series: | Series on advances in mathematics for applied sciences
58 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 239-248) |
| Physical Description: | XVIII, 248 S. graph. Darst. |
| ISBN: | 9810243057 |
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| 245 | 1 | 0 | |a Mechanical and thermodynamical modeling of fluid interfaces |c Renée Gatignol ; Roger Prud'homme |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2001 | |
| 300 | |a XVIII, 248 S. |b graph. Darst. | ||
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| 650 | 4 | |a Interfaces gaz-liquide - Modèles mathématiques | |
| 650 | 4 | |a Interfaces liquide-liquide - Modèles mathématiques | |
| 650 | 4 | |a Mathematisches Modell | |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
PREFACE v
LIST OF SYMBOLS xiii
1. INTRODUCTION 1
1.1. The concept of an interface 2
1.2. The concept of an interfacial layer 3
1.3. Presentation of the volume 4
2. THERMODYNAMICS AND KINEMATICS OF INTERFACES 7
2.1. Definition of surfaces 8
2.2. Interfacial quantities 10
2.3. Thermodynamic relations 12
2.3.1. The bulk 13
2.3.2. The interface 15
2.3.3. Thermodynamic equilibrium between two phases at rest 17
2.3.4. Surface tension out of equilibrium 20
2.4. Velocities and deformation rates of the interface 21
2.4.1. Material velocities in the bulk 21
2.4.2. Interfacial velocities in intrinsic description 21
2.4.3. Velocities in orthogonal curvilinear coordinates 23
2.4.4. Strain rates 26
2.4.5. Transport theorem for a curvilinear integral 27
2.4.6. Transport theorem for a surface integral 27
2.4.7. Divergence theorem on a surface 28
2.4.8. Interfacial fluxes 29
2.5. Examples 30
2.5.1. Effect of curvature on surface integrals 30
2.5.2. Parallel curves 32
vii
viii Mechanical and Thermodynamkal Modeling of Fluid Interfaces ,
2.5.3. Parallel surfaces 33
2.5.4. Effect of curvature on lateral surface integrals in the case
of parallel surfaces 34
2.5.5. Effect of curvature on equilibrium surface tension 36
2.5.6. Determination of the mean normal curvature 38
2.5.7. Deformation along a surface 39
2.5.8. Stretch of a moving cylinder 39
2.5.9. Stretch of a planar flame 41 .
3. INTERFACE BALANCE LAWS 43
3.1. General interface balance law 44
3.1.1. Balance law for the three dimensional continuum 44
3.1.2. First integration method of the local balance laws for
the three dimensional continuum 45
3.1.3. Second integration method of the balance laws for
the three dimensional continuum 51
3.1.4. Some comments 54
3.2. Interface balance laws for species, mass, momentum and energy 56
3.2.1. Interface balance laws for species 56
3.2.2. Interface balance law for mass 57
3.2.3. Momentum interface balance law 58
3.2.4. Energy interface balance law 60
3.3. Interfacial entropy production 62
3.3.1. Interfacial entropy inequality 62
3.3.2. Interface Clausius Duhem inequality 65
3.3.3. Balance laws for an interface inside one component fluids 68
3.3.4. A remark for the interfaces without mass 69
4. CONSTITUTIVE RELATIONS DEDUCED FROM LINEAR
IRREVERSIBLE THERMODYNAMICS FOR THE
TWO DIMENSIONAL INTERFACES 73
4.1. Analysis of the surface entropy production and possible coupling 73
4.2. Capillarity at equilibrium 75
4.3. Newtonian interface and surface viscosities 78
4.3.1. Benard Marangoni effect 78
4.3.2. Surface viscosities 78
4.4. Surface heat transfer 79
4.5. Problems related to evaporation / condensation 81
4.5.1. Plane interface case 81
4.5.2. Curvature effect 84
4.6. Surface chemical reactions 85
4.7 Interfaces without mass 87 (
Contents ix
5. CLASSICAL THREE DIMENSIONAL CONSTITUTIVE
RELATIONS DEDUCED FROM LINEAR IRREVERSIBLE
THERMODYNAMICS AND THEIR CONSEQUENCES FOR
INTERFACES 91
5.1. Constitutive relations of three dimensional classical fluid mixtures 92
5.2. The case of premixed flames with high activation energy 95
5.2.1. The classical theory of planar adiabatic premixed flames 96
5.2.2. Curved premixed flames with high activation energy for
Lewis number near unity 101
5.3. The case of shock waves and relaxation zones behind shock waves 108
5.3.1. The gaseous shock wave as an interface 108
5.3.2. Shock wave in a dusty gas 114
6. SECOND GRADIENT THEORY APPLIED TO INTERFACIAL MEDIUM 125
6.1. Description of a fluid with internal capillarity 126
6.1.1. Balance law for the mass 126
6.1.2. Virtual power principle 126
6.1.3. Boundary conditions on a wall 129
6.1.4. Balance energy law 132
6.1.5. Entropy inequality and Clausius Duhem inequality 133
6.1.6. Expression for the specific internal energy 133
6.2. A set of equations for a fluid with capillarity 135
6.2.1. Constitutive laws 135
6.2.2. Equation system for the description of a fluid with capillarity 137
6.3. Asymptotic modelization of an interface without mass 138
6.3.1. Order of magnitude analysis 140
6.3.2. Analysis of the interface balance laws 141
6.4. An expression for the surface tension 144
6.5. Description of a mixture of fluids with internal capillarity 146
6.5.1. Balance law for the mass of the N species 146
6.5.2. Virtual power principle for the mixture 147
6.5.3. Balance internal energy 149
6.5.4. Entropy inequality and Clausius Duhem inequality 150
6.5.5. Expression for the specific internal energy 150
6.5.6. A set of equations for a mixture of fluids with capillarity 153
7. TYPICAL PROBLEMS INVOLVING SURFACE TENSION AND
OTHER SURFACE PROPERTIES 157
7.1. The growth of a bubble 158
7.2. An interface with a surface viscosity 163
7.3. An interface with a variable surface tension 166
7.4. Marangoni instability 0
x Mechanical and Thermodynamical Modeling of Fluid Interfaces
7.4.1. Planar surface 171
7.4.2. Free surface 175
7.5. Vapor recoil 177
7.5.1. The Palmer analysis of the Hickman instability 177
7.5.2. The case of a mixture 183
7.5.3. Boiling crisis 186
7.6. Diffusive interfaces 190
7.6.1. Rayleigh Taylor and Kelvin Helmholtz instabilities 190
7.6.2. Linearized theory of interfacial layer instability between two i
heavy miscible fluids 195
7.6.3. Interfacial layer instability in a pure heated supercritical fluid 199
7.6.4. Linearized study of shear layers 200
A.l. TENSORIAL NOTATIONS 205
A.2. GEOMETRY OF INTERFACES AND INTERFACIAL LAYERS IN
ORTHOGONAL CURVILINEAR COORDINATES 209
A2.1. Definition of the surfaces 209
A2.2. Curvilinear coordinates 210
A2.3. Curl of a vector field 211
A2.4. Divergence of a vector field 212
A2.5. Gradient of a scalar field 213
A2.6. Laplacian of a scalar field 213
A2.7. Differentiation of curvilinear basis 213
A2.8. Divergence of a second order tensor field P 214
A2.9. Gradient of a vector 215
A2.10. Projection operators 215
A2.ll. Surface gradients of a scalar field 216
A2.12. Curvature vector of a curve C; 216
A2.13. Definitions of normal and tangential divergences of a vector field 217
A2.14. Surface stretch per unit length 217
A2.15. Mean normal curvature of a surface 218
A2.16. Decomposition of the divergence of a vector field 219
A2.17. Decomposition of the Laplacian of a scalar field 220
A2.18. Decomposition of the divergence of a second order tensor field 221
A2.19. Parallel divergence of the product V • P for a particular class of
tensors P 223
A2.20. Intrinsic definition of a surface 223
A2.21. Comparison between the two descriptions 224
A2.22. Family of parallel surfaces 226
A2.23. Variation of the parallel divergence of a vector across an interfacial Iayer228
Contents xi
A.3. KINEMATICS OF THE INTERFACE 231
A3.1. Velocities in intrinsic description 231
A3.2. Velocities in orthogonal curvilinear coordinates 232
A3.3. Strain rates 233
A3.4. Parallel surfaces 235
A3.5. Stretching rate of a surface 235
A3.6. Stretch variation across interfacial layer 236
BIBLIOGRAPHY 239
|
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| indexdate | 2024-07-09T19:03:00Z |
| institution | BVB |
| isbn | 9810243057 |
| language | English |
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| spelling | Gatignol, Renée Verfasser aut Mechanical and thermodynamical modeling of fluid interfaces Renée Gatignol ; Roger Prud'homme Singapore [u.a.] World Scientific 2001 XVIII, 248 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Series on advances in mathematics for applied sciences 58 Includes bibliographical references (p. 239-248) Interfaces (Sciences physiques) - Thermodynamique - Modèles mathématiques Interfaces gaz-liquide - Modèles mathématiques Interfaces liquide-liquide - Modèles mathématiques Mathematisches Modell Gas-liquid interfaces Mathematical models Interfaces (Physical sciences) Thermodynamics Mathematical models Liquid-liquid interfaces Mathematical models Grenzfläche (DE-588)4021991-4 gnd rswk-swf Flüssigkeit (DE-588)4017621-6 gnd rswk-swf Modellierung (DE-588)4170297-9 gnd rswk-swf Flüssigkeit (DE-588)4017621-6 s Grenzfläche (DE-588)4021991-4 s Modellierung (DE-588)4170297-9 s DE-604 Prud'homme, Roger Sonstige oth Series on advances in mathematics for applied sciences 58 (DE-604)BV004569239 58 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009878658&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gatignol, Renée Mechanical and thermodynamical modeling of fluid interfaces Series on advances in mathematics for applied sciences Interfaces (Sciences physiques) - Thermodynamique - Modèles mathématiques Interfaces gaz-liquide - Modèles mathématiques Interfaces liquide-liquide - Modèles mathématiques Mathematisches Modell Gas-liquid interfaces Mathematical models Interfaces (Physical sciences) Thermodynamics Mathematical models Liquid-liquid interfaces Mathematical models Grenzfläche (DE-588)4021991-4 gnd Flüssigkeit (DE-588)4017621-6 gnd Modellierung (DE-588)4170297-9 gnd |
| subject_GND | (DE-588)4021991-4 (DE-588)4017621-6 (DE-588)4170297-9 |
| title | Mechanical and thermodynamical modeling of fluid interfaces |
| title_auth | Mechanical and thermodynamical modeling of fluid interfaces |
| title_exact_search | Mechanical and thermodynamical modeling of fluid interfaces |
| title_full | Mechanical and thermodynamical modeling of fluid interfaces Renée Gatignol ; Roger Prud'homme |
| title_fullStr | Mechanical and thermodynamical modeling of fluid interfaces Renée Gatignol ; Roger Prud'homme |
| title_full_unstemmed | Mechanical and thermodynamical modeling of fluid interfaces Renée Gatignol ; Roger Prud'homme |
| title_short | Mechanical and thermodynamical modeling of fluid interfaces |
| title_sort | mechanical and thermodynamical modeling of fluid interfaces |
| topic | Interfaces (Sciences physiques) - Thermodynamique - Modèles mathématiques Interfaces gaz-liquide - Modèles mathématiques Interfaces liquide-liquide - Modèles mathématiques Mathematisches Modell Gas-liquid interfaces Mathematical models Interfaces (Physical sciences) Thermodynamics Mathematical models Liquid-liquid interfaces Mathematical models Grenzfläche (DE-588)4021991-4 gnd Flüssigkeit (DE-588)4017621-6 gnd Modellierung (DE-588)4170297-9 gnd |
| topic_facet | Interfaces (Sciences physiques) - Thermodynamique - Modèles mathématiques Interfaces gaz-liquide - Modèles mathématiques Interfaces liquide-liquide - Modèles mathématiques Mathematisches Modell Gas-liquid interfaces Mathematical models Interfaces (Physical sciences) Thermodynamics Mathematical models Liquid-liquid interfaces Mathematical models Grenzfläche Flüssigkeit Modellierung |
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