Mechanic and Thermodynamic Modeling of Fluid Interfaces

R. Gatignol, R. Prud’Homme9810243057, 9789810243050, 9789812810625

This book constitutes a comprehensive survey of the balance equations for mass, momentum and energy for the interfaces in pure fluids and mixtures. Constitutive laws are presented for many situations in engineering science, and examples are provided, including surface viscosity effects, variable surface tension and vapor recoil. In addition, some extensions of existing theory are given: stretch effect in premixed flames, relaxation zones downstream two-phase shock waves, and effective surface tension for steep gradient zones.

---

Table of contents :
PREFACE……Page p0006.djvu
CONTENTS……Page p0008.djvu
LIST OF SYMBOLS……Page p0014.djvu
1. INTRODUCTION……Page p0020.djvu
1.1. The concept of an “interface”……Page p0021.djvu
1.2. The concept of an “interfacial layer”……Page p0022.djvu
1.3. Presentation of the volume……Page p0023.djvu
2. THERMODYNAMICS AND KINEMATICS OF INTERFACES……Page p0026.djvu
2.1. Definition of surfaces……Page p0027.djvu
2.2. Interfacial quantities……Page p0029.djvu
2.3. Thermodynamic relations……Page p0031.djvu
2.3.1. The bulk……Page p0032.djvu
2.3.2. The interface……Page p0034.djvu
2.3.3. Thermodynamic equilibrium between two phases at rest……Page p0036.djvu
2.3.4. Surface tension out of equilibrium……Page p0039.djvu
2.4.2. Interfacial velocities in intrinsic description……Page p0040.djvu
2.4.3. Velocities in orthogonal curvilinear coordinates……Page p0042.djvu
2.4.4. Strain rates……Page p0045.djvu
2.4.6. Transport theorem for a surface integral……Page p0046.djvu
2.4.7. Divergence theorem on a surface……Page p0047.djvu
2.4.8. Interfacial fluxes……Page p0048.djvu
2.5.1. Effect of curvature on surface integrals……Page p0049.djvu
2.5.2. Parallel curves……Page p0051.djvu
2.5.3. Parallel surfaces……Page p0052.djvu
2.5.4. Effect of curvature on lateral surface integrals in the case of parallel surfaces……Page p0053.djvu
2.5.5. Effect of curvature on equilibrium surface tension……Page p0055.djvu
2.5.6. Determination of the mean normal curvature……Page p0057.djvu
2.5.8. Stretch of a moving cylinder……Page p0058.djvu
2.5.9. Stretch of a planar flame……Page p0060.djvu
3. INTERFACE BALANCE LAWS……Page p0062.djvu
3.1.1. Balance law for the three-dimensional continuum……Page p0063.djvu
3.1.2. First integration method of the local balance laws for the three-dimensional continuum……Page p0064.djvu
3.1.3. Second integration method of the balance laws for the three-dimensional continuum……Page p0070.djvu
3.1.4. Some comments……Page p0073.djvu
3.2.1. Interface balance laws for species……Page p0075.djvu
3.2.2. Interface balance law for mass……Page p0076.djvu
3.2.3. Momentum interface balance law……Page p0077.djvu
3.2.4. Energy interface balance law……Page p0079.djvu
3.3.1. Interfacial entropy inequality……Page p0081.djvu
3.3.2. Interface Clausius-Duhem inequality……Page p0084.djvu
3.3.3. Balance laws for an interface inside one component fluids……Page p0087.djvu
3.3.4. A remark for the interfaces without mass……Page p0088.djvu
4.1. Analysis of the surface entropy production and possible coupling……Page p0092.djvu
4.2. Capillarity at equilibrium……Page p0094.djvu
4.3.2. Surface viscosities……Page p0097.djvu
4.4. Surface heat transfer……Page p0098.djvu
4.5.1. Plane interface case……Page p0100.djvu
4.5.2. Curvature effect……Page p0103.djvu
4.6. Surface chemical reactions……Page p0104.djvu
4.7 Interfaces without mass……Page p0106.djvu
5. CLASSICAL THREE-DIMENSIONAL CONSTITUTIVE RELATIONS DEDUCED FROM LINEAR IRREVERSIBLE THERMODYNAMICS AND THEIR CONSEQUENCES FOR INTERFACES……Page p0110.djvu
5.1. Constitutive relations of three-dimensional classical fluid mixtures……Page p0111.djvu
5.2. The case of premixed flames with high activation energy……Page p0114.djvu
5.2.1. The classical theory of planar adiabatic premixed flames……Page p0115.djvu
5.2.2. Curved premixed flames with high activation energy for Lewis number near unity……Page p0120.djvu
5.3.1. The gaseous shock wave as an interface……Page p0127.djvu
5.3.2. Shock wave in a dusty gas……Page p0133.djvu
6. SECOND GRADIENT THEORY APPLIED TO INTERFACIAL MEDIUM……Page p0144.djvu
6.1.2. Virtual power principle……Page p0145.djvu
6.1.3. Boundary conditions on a wall……Page p0148.djvu
6.1.4. Balance energy law……Page p0151.djvu
6.1.6. Expression for the specific internal energy……Page p0152.djvu
6.2.1. Constitutive laws……Page p0154.djvu
6.2.2. Equation system for the description of a fluid with capillarity……Page p0156.djvu
6.3. Asymptotic modelization of an interface without mass……Page p0157.djvu
6.3.1. Order of magnitude analysis……Page p0159.djvu
6.3.2. Analysis of the interface balance laws……Page p0160.djvu
6.4. An expression for the surface tension……Page p0163.djvu
6.5.1. Balance law for the mass of the N species……Page p0165.djvu
6.5.2. Virtual power principle for the mixture……Page p0166.djvu
6.5.3. Balance internal energy……Page p0168.djvu
6.5.5. Expression for the specific internal energy……Page p0169.djvu
6.5.6. A set of equations for a mixture of fluids with capillarity……Page p0172.djvu
7. TYPICAL PROBLEMS INVOLVING SURFACE TENSION AND OTHER SURFACE PROPERTIES……Page p0176.djvu
7.1. The growth of a bubble……Page p0177.djvu
7.2. An interface with a surface viscosity……Page p0182.djvu
7.3. An interface with a variable surface tension……Page p0185.djvu
7.4. Marangoni instability……Page p0189.djvu
7.4.1. Planar surface……Page p0190.djvu
7.4.2. Free surface……Page p0194.djvu
7.5.1. The Palmer analysis of the Hickman instability……Page p0196.djvu
7.5.2. The case of a mixture……Page p0202.djvu
7.5.3. Boiling crisis……Page p0205.djvu
7.6.1. Rayleigh-Taylor and Kelvin-Helmholtz instabilities……Page p0209.djvu
7.6.2. Linearized theory of interfacial layer instability between two heavy miscible fluids……Page p0214.djvu
7.6.3. Interfacial layer instability in a pure heated supercritical fluid……Page p0218.djvu
7.6.4. Linearized study of shear layers……Page p0219.djvu
A.1. TENSORIAL NOTATIONS……Page p0224.djvu
A2.1. Definition of the surfaces……Page p0228.djvu
A2.2. Curvilinear coordinates……Page p0229.djvu
A2.3. Curl of a vector field……Page p0230.djvu
A2.4. Divergence of a vector field……Page p0231.djvu
A2.7. Differentiation of curvilinear basis……Page p0232.djvu
A2.8. Divergence of a second order tensor field P……Page p0233.djvu
A2.10. Projection operators……Page p0234.djvu
A2.12. Curvature vector of a curve Ci……Page p0235.djvu
A2.14. Surface stretch per unit length……Page p0236.djvu
A2.15. Mean normal curvature of a surface……Page p0237.djvu
A2.16. Decomposition of the divergence of a vector field……Page p0238.djvu
A2.17. Decomposition of the Laplacian of a scalar field……Page p0239.djvu
A2.18. Decomposition of the divergence of a second order tensor field……Page p0240.djvu
A2.20. Intrinsic definition of a surface……Page p0242.djvu
A2.21. Comparison between the two descriptions……Page p0243.djvu
A2.22. Family of parallel surfaces……Page p0245.djvu
A2.23. Variation of the parallel divergence of a vector across an interfacial layer……Page p0247.djvu
A3.1. Velocities in intrinsic description……Page p0250.djvu
A3.2. Velocities in orthogonal curvilinear coordinates……Page p0251.djvu
A3.3. Strain rates……Page p0252.djvu
A3.5. Stretching rate of a surface……Page p0254.djvu
A3.6. Stretch variation across interfacial layer……Page p0255.djvu
BIBLIOGRAPHY……Page p0258.djvu