This book deals with density, temperature, velocity and concentration fluctuations in fluids and fluid mixtures. The book first reviews thermal fluctuations in equilibrium fluids on the basis of fluctuating hydrodynamics. It then shows how the method of fluctuating hydrodynamics can be extended to deal with hydrodynamic fluctuations when the system is in a stationary nonequilibrium state. In contrast to equilibrium fluids where the fluctuations are generally short ranged unless the system is close to a critical point, fluctuations in nonequilibrium fluids are always long-ranged encompassing the entire system. The book provides the first comprehensive treatment of fluctuations in fluids and fluid mixtures brought out of equilibrium by the imposition of a temperature and concentration gradient but that are still in a macroscopically quiescent state. By incorporating appropriate boundary conditions in the case of fluid layers, it is shown how fluctuating hydrodynamics affects the fluctuations close to the onset of convection. Experimental techniques of light scattering and shadowgraphy for measuring nonequilibrium fluctuations are elucidated and the experimental results thus far reported in the literature are reviewed.* Systematic exposition of fluctuating hydrodynamics and its applications* First book on nonequilibrium fluctuations in fluids* Fluctuating Boussinesq equations and nonequilibrium fluids* Fluid layers and onset of convection* Rayleigh scattering and Brillouin scattering in fluids* Shadowgraph technique for measuring fluctuations* Fluctuations near hydrodynamic instabilities
Author(s): Jose M. Ortiz de Zarate Doctor en Ciencias Fisicas Universidad Complutense 1991, Jan V. Sengers Ph.D. University of Amsterdam 1962
Doctor Honoris Causa Technical University Delft 1992
Edition: 1
Publisher: Elsevier Science
Year: 2006
Language: English
Pages: 321
Tags: Механика;Механика жидкостей и газов;Гидромеханика;
Hydrodynamic Fluctuations in Fluids and Fluid Mixtures......Page 4
Preface......Page 6
Contents......Page 8
Introduction......Page 12
Equilibrium thermodynamics......Page 16
Continuum hypothesis and the assumption of local equilibrium......Page 18
Balance laws......Page 19
Mass balance......Page 20
Pressure tensor......Page 22
Momentum balance......Page 26
Energy balance......Page 27
Additional remarks......Page 30
Entropy balance, dissipative .uxes and thermodynamic forces......Page 31
Phenomenological relations......Page 33
Onsager’s reciprocal relations......Page 34
Hydrodynamic equations for a one-component .uid......Page 35
Hydrodynamic equations for a binary mixture......Page 39
Conditions at the interface between two continuous media......Page 44
A flat horizontal fluid boundary......Page 47
Fluctuations in fluids in thermodynamic equilibrium......Page 50
Fluctuating hydrodynamics......Page 51
Fluctuation-dissipation theorem for a one-component .uid......Page 54
Fluctuation-dissipation theorem for a binary mixture......Page 56
Hydrodynamic fluctuations in a one-component .uid......Page 57
Structure factor......Page 62
Equal-time correlations......Page 65
Equilibrium correlation functions and entropy probability functional......Page 67
Extension of fluctuating hydrodynamics to nonequilibrium steady states......Page 71
Thermal nonequilibrium fluctuations in one-component fluids......Page 74
Boussinesq approximation......Page 75
Bulk structure factor in the presence of a stationary temperature gradient......Page 81
Nonequilibrium e.ects on the Brillouin doublet......Page 87
Nonequilibrium fluctuations in heat conduction......Page 93
Thermal nonequilibrium fluctuations in fluid mixtures......Page 100
Linearized fluctuating Boussinesq equations for a binary liquid......Page 102
The linear stability problem......Page 105
Structure factor in a large-Lewis-number approximation......Page 108
Comprehensive structure factor of a nonequilibrium binary mixture......Page 113
Nonequilibrium .uctuations in isothermal free-di.usion processes......Page 121
Finite-size effects in hydrodynamic fluctuations......Page 124
The hydrodynamic operator......Page 126
Structure factors......Page 133
Hydrodynamic modes and decay rates for two free boundaries......Page 136
Hydrodynamic modes and decay rates for two rigid boundaries......Page 140
Decay rates for rigid boundaries in the limit of small q......Page 142
Decay rates for rigid boundaries in the limit of large q......Page 145
The slowest decay rate......Page 147
Thermal nonequilibrium fluctuations in one-component- fluid layers......Page 152
A fluid confined between two free boundaries......Page 153
A fluid confined between two rigid boundaries......Page 158
Limiting behavior of the structure factor for rigid boundaries at small and large wave numbers......Page 163
A Galerkin approximation for two rigid boundaries......Page 166
Correlations in real space......Page 173
Contribution of nonequilibrium fluctuations to heat transfer......Page 177
Thermal fluctuations close to the Rayleigh-B´enard instability......Page 178
Critical slowing down of nonequilibrium fluctuations......Page 179
The most-unstable-mode approximation......Page 180
The Swift-Hohenberg approximation......Page 183
Power of thermal fluctuations......Page 186
Wave number of maximum enhancement of .uctuations......Page 190
Wave number fluctuations with maximum growth rate......Page 192
Thermal nonequilibrium fluctuations in binary-fluid layers......Page 196
The hydrodynamic operator for binary Boussinesq......Page 198
A Galerkin approximation for rigid and impermeable boundary conditions......Page 200
Evaluation of nonequilibrium structure factors......Page 205
Structure factor in thermal equilibrium......Page 208
Nonequilibrium fluctuations for positive separation ratio......Page 209
Temperature fluctuations......Page 210
Concentration fluctuations......Page 215
Large-Lewis-number approximation for positive separation ratio......Page 218
Concluding remarks......Page 222
Experiments on nonequilibrium fluctuations in the Rayleigh- B´enard problem......Page 224
Small-angle light scattering......Page 225
Quantitative shadowgraph analysis......Page 233
Dependence of shadowgraph images on collecting times......Page 239
Propagating modes .......Page 240
Brillouin doublet......Page 241
Rayleigh scattering......Page 243
Divergence of critical fluctuations near the onset of convection......Page 246
Critical slowing down of fluctuations near the onset of convection......Page 248
Light scattering in binary systems......Page 250
Nonequilibrium fluctuations in liquid mixtures......Page 251
Concentration fluctuations in dilute polymer solutions......Page 254
Shadowgraphy in binary mixtures......Page 257
Other nonequilibrium fluctuations......Page 258
Nonequilibrium fluctuations in isothermal one-component fluids under shear......Page 259
Nonequilibrium interface fluctuations......Page 263
Nonequilibrium fluctuations in nematic liquid crystals......Page 264
Concentration fluctuations in reaction-diffusion problems .......Page 267
Equilibrium concentration fluctuations in reaction-diffusion......Page 268
Nonequilibrium concentration fluctuations in reaction-diffusion......Page 274
Epilogue......Page 280
Bibliography......Page 284
List of symbols and corresponding SI units......Page 308
List of abbreviations......Page 314
Subject index......Page 316
