Cover image for Hydrodynamic Fluctuations in Fluids and Fluid Mixtures.
Hydrodynamic Fluctuations in Fluids and Fluid Mixtures.
Title:
Hydrodynamic Fluctuations in Fluids and Fluid Mixtures.
Author:
Ortiz de Zarate, Jose M.
ISBN:
9780080459431
Personal Author:
Edition:
1st ed.
Physical Description:
1 online resource (321 pages)
Contents:
Front cover -- Title page -- Copyright -- Front matter -- Preface -- Table of contents -- Body -- 1 Introduction -- 2 Nonequilibrium thermodynamics -- Local thermodynamic properties -- Equilibrium thermodynamics -- Continuum hypothesis and the assumption of local equilibrium -- Balance laws -- Mass balance -- Pressure tensor -- Momentum balance -- Energy balance -- Additional remarks -- Entropy balance, dissipative fluxes and thermodynamic forces -- Phenomenological relations -- Onsager's reciprocal relations -- Hydrodynamic equations -- Hydrodynamic equations for a one-component fluid -- Hydrodynamic equations for a binary mixture -- Boundary conditions -- Conditions at the interface between two continuous media -- A flat horizontal fluid boundary -- 3 Fluctuations in fluids in thermodynamic equilibrium -- Fluctuating hydrodynamics -- Fluctuation-dissipation theorem for fluids and fluid mixtures -- Fluctuation-dissipation theorem for a one-component fluid -- Fluctuation-dissipation theorem for a binary mixture -- Hydrodynamic fluctuations in a one-component fluid -- Structure factor -- Equal-time correlations -- Equilibrium correlation functions and entropy probability functional -- Extension of fluctuating hydrodynamics to nonequilibrium steady states -- 4 Thermal nonequilibrium fluctuations in one-component fluids -- Boussinesq approximation -- Bulk structure factor in the presence of a stationary temperature gradient -- Nonequilibrium effects on the Brillouin doublet -- Nonequilibrium fluctuations in heat conduction -- 5 Thermal nonequilibrium fluctuations in fluid mixtures -- Linearized fluctuating Boussinesq equations for a binary liquid -- The linear stability problem -- Structure factor in a large-Lewis-number approximation -- Comprehensive structure factor of a nonequilibrium binary mixture.

Nonequilibrium fluctuations in isothermal free-diffusion processes -- 6 Finite-size effects in hydrodynamic fluctuations -- The hydrodynamic operator -- Structure factors -- Hydrodynamic modes and decay rates for two free boundaries -- Hydrodynamic modes and decay rates for two rigid boundaries -- Decay rates for rigid boundaries in the limit of small q -- Decay rates for rigid boundaries in the limit of large q -- The slowest decay rate -- 7 Thermal nonequilibrium fluctuations in one-component-fluid layers -- A fluid confined between two free boundaries -- A fluid confined between two rigid boundaries -- Limiting behavior of the structure factor for rigid boundaries at small and large wave numbers -- A Galerkin approximation for two rigid boundaries -- Correlations in real space -- Contribution of nonequilibrium fluctuations to heat transfer -- 8 Thermal fluctuations close to the Rayleigh-Bénard instability -- Critical slowing down of nonequilibrium fluctuations -- The most-unstable-mode approximation -- The Swift-Hohenberg approximation -- Power of thermal fluctuations -- Wave number of maximum enhancement of fluctuations -- Wave number fluctuations with maximum growth rate -- 9 Thermal nonequilibrium fluctuations in binary-fluid layers -- The hydrodynamic operator for binary Boussinesq -- A Galerkin approximation for rigid and impermeable boundary conditions -- Evaluation of nonequilibrium structure factors -- Structure factor in thermal equilibrium -- Nonequilibrium fluctuations for positive separation ratio -- Temperature fluctuations -- Concentration fluctuations -- Large-Lewis-number approximation for positive separation ratio -- Concluding remarks -- 10 Experiments on nonequilibrium fluctuations in the Rayleigh-Bénard problem -- Experimental techniques -- Small-angle light scattering -- Quantitative shadowgraph analysis.

Dependence of shadowgraph images on collecting times -- Nonequilibrium light-scattering experiments in one-component fluids -- Propagating modes -- Brillouin doublet -- Rayleigh scattering -- Shadowgraph experiments in one-component fluids -- Divergence of critical fluctuations near the onset of convection -- Critical slowing down of fluctuations near the onset of convection -- Light scattering in binary systems -- Nonequilibrium fluctuations in liquid mixtures -- Concentration fluctuations in dilute polymer solutions -- Shadowgraphy in binary mixtures -- 11 Other nonequilibrium fluctuations -- Nonequilibrium fluctuations in isothermal one-component fluids under shear -- Nonequilibrium interface fluctuations -- Nonequilibrium fluctuations in nematic liquid crystals -- Concentration fluctuations in reaction-diffusion problems -- Equilibrium concentration fluctuations in reaction-diffusion -- Nonequilibrium concentration fluctuations in reaction-diffusion -- 12 Epilogue -- Back matter -- Bibliography -- List of symbols and corresponding SI units -- List of abbreviations -- Index.
Abstract:
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.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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