Hydrodynamic Fluctuations in Fluids and Fluid Mixtures (eBook)

Cover 1
Contents 8
Introduction 12
Nonequilibrium thermodynamics 16
Local thermodynamic properties 16
Equilibrium thermodynamics 16
Continuum hypothesis and the assumption of local equilibrium 18
Balance laws 19
Mass balance 20
Pressure tensor 22
Momentum balance 26
Energy balance 27
Additional remarks 30
Entropy balance, dissipative Fluxes and thermodynamic forces 31
Phenomenological relations 33
Onsager’s reciprocal relations 34
Hydrodynamic equations 35
Hydrodynamic equations for a one-component Fluid 35
Hydrodynamic equations for a binary mixture 39
Boundary conditions 44
Conditions at the interface between two continuous media 44
A flat horizontal fluid boundary 47
Fluctuations in fluids in thermodynamic equilibrium 50
Fluctuating hydrodynamics 51
Fluctuation-dissipation theorem for Fluids and Fluid mixtures 54
Fluctuation-dissipation theorem for a one-component Fluid 54
Fluctuation-dissipation theorem for a binary mixture 56
Hydrodynamic fluctuations in a one-component Fluid 57
Structure factor 62
Equal-time correlations 65
Equilibrium correlation functions and entropy probability functional 67
Extension of fluctuating hydrodynamics to nonequilibrium steady states 71
Thermal nonequilibrium fluctuations in one-component fluids 74
Boussinesq approximation 75
Bulk structure factor in the presence of a stationary temperature gradient 81
Nonequilibrium e.ects on the Brillouin doublet 87
Nonequilibrium fluctuations in heat conduction 93
Thermal nonequilibrium fluctuations in fluid mixtures 100
Linearized fluctuating Boussinesq equations for a binary liquid 102
The linear stability problem 105
Structure factor in a large-Lewis-number approximation 108
Comprehensive structure factor of a nonequilibrium binary mixture 113
Nonequilibrium .uctuations in isothermal free-di.usion processes 121
Finite-size effects in hydrodynamic fluctuations 124
The hydrodynamic operator 126
Structure factors 133
Hydrodynamic modes and decay rates for two free boundaries 136
Hydrodynamic modes and decay rates for two rigid boundaries 140
Decay rates for rigid boundaries in the limit of small q 142
Decay rates for rigid boundaries in the limit of large q 145
The slowest decay rate 147
Thermal nonequilibrium fluctuations in one-component- fluid layers 152
A fluid confined between two free boundaries 153
A fluid confined between two rigid boundaries 158
Limiting behavior of the structure factor for rigid boundaries at small and large wave numbers 163
A Galerkin approximation for two rigid boundaries 166
Correlations in real space 173
Contribution of nonequilibrium fluctuations to heat transfer 177
Thermal fluctuations close to the Rayleigh-Benard instability 178
Critical slowing down of nonequilibrium fluctuations 179
The most-unstable-mode approximation 180
The Swift-Hohenberg approximation 183
Power of thermal fluctuations 186
Wave number of maximum enhancement of .uctuations 190
Wave number fluctuations with maximum growth rate 192
Thermal nonequilibrium fluctuations in binary-fluid layers 196
The hydrodynamic operator for binary Boussinesq 198
A Galerkin approximation for rigid and impermeable boundary conditions 200
Evaluation of nonequilibrium structure factors 205
Structure factor in thermal equilibrium 208
Nonequilibrium fluctuations for positive separation ratio 209
Temperature fluctuations 210
Concentration fluctuations 215
Large-Lewis-number approximation for positive separation ratio 218
Concluding remarks 222
Experiments on nonequilibrium fluctuations in the Rayleigh- Benard problem 224
Experimental techniques 225
Small-angle light scattering 225
Quantitative shadowgraph analysis 233
Dependence of shadowgraph images on collecting times 239
Nonequilibrium light-scattering experiments in one-component Fluids 240
Propagating modes 240
Brillouin doublet 241
Rayleigh scattering 243
Shadowgraph experiments in one-component Fluids 246
Divergence of critical fluctuations near the onset of convection 246
Critical slowing down of fluctuations near the onset of convection 248
Light scattering in binary systems 250
Nonequilibrium fluctuations in liquid mixtures 251
Concentration fluctuations in dilute polymer solutions 254
Shadowgraphy in binary mixtures 257
Other nonequilibrium fluctuations 258
Nonequilibrium fluctuations in isothermal one-component fluids under shear 259
Nonequilibrium interface fluctuations 263
Nonequilibrium fluctuations in nematic liquid crystals 264
Concentration fluctuations in reaction-diffusion problems . 267
Equilibrium concentration fluctuations in reaction-diffusion 268
Nonequilibrium concentration fluctuations in reaction-diffusion 274
Epilogue 280
Bibliography 284
List of symbols and corresponding SI units 308
List of abbreviations 314
Subject index 316