# Hydrodynamic Fluctuations in Fluids and Fluid Mixtures

## 1st Edition

**Authors:**Jose Ortiz de Zarate Jan Sengers

**Paperback ISBN:**9780444515155

**eBook ISBN:**9780080459431

**Imprint:**Elsevier Science

**Published Date:**19th April 2006

**Page Count:**320

## Description

- Preface
- Chapter 1: Introduction
- Publisher Summary

- Chapter 2: Nonequilibrium thermodynamics
- Publisher Summary
- 2.1 Local thermodynamic properties
- 2.2 Balance laws
- 2.3 Entropy balance, dissipative fluxes and thermodynamic forces
- 2.4 Hydrodynamic equations
- 2.5 Boundary conditions

- Chapter 3: Fluctuations in fluids in thermodynamic equilibrium
- Publisher Summary
- 3.1 Fluctuating hydrodynamics
- 3.2 Fluctuation-dissipation theorem for fluids and fluid mixtures
- 3.3 Hydrodynamic fluctuations in a one-component fluid
- 3.4 Equilibrium correlation functions and entropy probability functional
- 3.5 Extension of fluctuating hydrodynamics to nonequilibrium steady states

- Chapter 4: Thermal nonequilibrium fluctuations in one-component fluids
- Publisher Summary
- 4.1 Boussinesq approximation
- 4.2 Bulk structure factor in the presence of a stationary temperature gradient
- 4.3 Nonequilibrium effects on the Brillouin doublet
- 4.4 Nonequilibrium fluctuations in heat conduction

- Chapter 5: Thermal nonequilibrium fluctuations in fluid mixtures
- Publisher Summary
- 5.1 Linearized fluctuating Boussinesq equations for a binary liquid
- 5.2 Structure factor in a large-Lewis-number approximation
- 5.3 Comprehensive structure factor of a nonequilibrium binary mixture
- 5.4 Nonequilibrium fluctuations in isothermal free-diffusion processes

- Chapter 6: Finite-size effects in hydrodynamic fluctuations
- Publisher Summary
- 6.1 The hydrodynamic operator
- 6.2 Hydrodynamic modes and decay rates for two free boundaries
- 6.3 Hydrodynamic modes and decay rates for two rigid boundaries
- 6.4 The slowest decay rate

- Chapter 7: Thermal nonequilibrium fluctuations in one-component-fluid layers
- Publisher Summary
- 7.1 A fluid confined between two free boundaries
- 7.2 A fluid confined between two rigid boundaries
- 7.3 Limiting behavior of the structure factor for rigid boundaries at small and large wave numbers
- 7.4 A Galerkin approximation for two rigid boundaries
- 7.5 Correlations in real space
- 7.6 Contribution of nonequilibrium fluctuations to heat transfer

- Chapter 8: Thermal fluctuations close to the Rayleigh-Bénard instability
- Publisher Summary
- 8.1 Critical slowing down of nonequilibrium fluctuations
- 8.2 The most-unstable-mode approximation
- 8.3 The Swift-Hohenberg approximation
- 8.4 Power of thermal fluctuations
- 8.5 Wave number of maximum enhancement of fluctuations
- 8.6 Wave number of fluctuations with maximum growth rate

- Chapter 9: Thermal nonequilibrium fluctuations in binary-fluid layers
- Publisher Summary
- 9.1 The hydrodynamic operator for binary Boussinesq
- 9.2 A Galerkin approximation for rigid and impermeable boundary conditions
- 9.3 Evaluation of nonequilibrium structure factors
- 9.4 Structure factor in thermal equilibrium
- 9.5 Nonequilibrium fluctuations for positive separation ratio
- 9.6 Large-Lewis-number approximation for positive separation ratio
- 9.7 Concluding remarks

- Chapter 10: Experiments on nonequilibrium fluctuations in the Rayleigh-Bénard problem
- Publisher Summary
- 10.1 Experimental techniques
- 10.2 Nonequilibrium light-scattering experiments in one-component fluids
- 10.3 Shadowgraph experiments in one-component fluids
- 10.4 Light scattering in binary systems
- 10.5 Shadowgraphy in binary mixtures

- Chapter 11: Other nonequilibrium fluctuations
- Publisher Summary
- 11.1 Nonequilibrium fluctuations in isothermal one-component fluids under shear
- 11.2 Nonequilibrium interface fluctuations
- 11.3 Nonequilibrium fluctuations in nematic liquid crystals
- 11.4 Concentration fluctuations in reaction-diffusion problems

- Chapter 12: Epilogue
- Publisher Summary

- Bibliography
- List of symbols and corresponding SI units
- List of abbreviations
- Subject index

## Key Features

· 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

## Readership

Physics, chemical physics, chemical engineering and Mechanical Engineering researchers

## Table of Contents

- Preface
- Chapter 1: Introduction
- Publisher Summary

- Chapter 2: Nonequilibrium thermodynamics
- Publisher Summary
- 2.1 Local thermodynamic properties
- 2.2 Balance laws
- 2.3 Entropy balance, dissipative fluxes and thermodynamic forces
- 2.4 Hydrodynamic equations
- 2.5 Boundary conditions

- Chapter 3: Fluctuations in fluids in thermodynamic equilibrium
- Publisher Summary
- 3.1 Fluctuating hydrodynamics
- 3.2 Fluctuation-dissipation theorem for fluids and fluid mixtures
- 3.3 Hydrodynamic fluctuations in a one-component fluid
- 3.4 Equilibrium correlation functions and entropy probability functional
- 3.5 Extension of fluctuating hydrodynamics to nonequilibrium steady states

- Chapter 4: Thermal nonequilibrium fluctuations in one-component fluids
- Publisher Summary
- 4.1 Boussinesq approximation
- 4.2 Bulk structure factor in the presence of a stationary temperature gradient
- 4.3 Nonequilibrium effects on the Brillouin doublet
- 4.4 Nonequilibrium fluctuations in heat conduction

- Chapter 5: Thermal nonequilibrium fluctuations in fluid mixtures
- Publisher Summary
- 5.1 Linearized fluctuating Boussinesq equations for a binary liquid
- 5.2 Structure factor in a large-Lewis-number approximation
- 5.3 Comprehensive structure factor of a nonequilibrium binary mixture
- 5.4 Nonequilibrium fluctuations in isothermal free-diffusion processes

- Chapter 6: Finite-size effects in hydrodynamic fluctuations
- Publisher Summary
- 6.1 The hydrodynamic operator
- 6.2 Hydrodynamic modes and decay rates for two free boundaries
- 6.3 Hydrodynamic modes and decay rates for two rigid boundaries
- 6.4 The slowest decay rate

- Chapter 7: Thermal nonequilibrium fluctuations in one-component-fluid layers
- Publisher Summary
- 7.1 A fluid confined between two free boundaries
- 7.2 A fluid confined between two rigid boundaries
- 7.3 Limiting behavior of the structure factor for rigid boundaries at small and large wave numbers
- 7.4 A Galerkin approximation for two rigid boundaries
- 7.5 Correlations in real space
- 7.6 Contribution of nonequilibrium fluctuations to heat transfer

- Chapter 8: Thermal fluctuations close to the Rayleigh-Bénard instability
- Publisher Summary
- 8.1 Critical slowing down of nonequilibrium fluctuations
- 8.2 The most-unstable-mode approximation
- 8.3 The Swift-Hohenberg approximation
- 8.4 Power of thermal fluctuations
- 8.5 Wave number of maximum enhancement of fluctuations
- 8.6 Wave number of fluctuations with maximum growth rate

- Chapter 9: Thermal nonequilibrium fluctuations in binary-fluid layers
- Publisher Summary
- 9.1 The hydrodynamic operator for binary Boussinesq
- 9.2 A Galerkin approximation for rigid and impermeable boundary conditions
- 9.3 Evaluation of nonequilibrium structure factors
- 9.4 Structure factor in thermal equilibrium
- 9.5 Nonequilibrium fluctuations for positive separation ratio
- 9.6 Large-Lewis-number approximation for positive separation ratio
- 9.7 Concluding remarks

- Chapter 10: Experiments on nonequilibrium fluctuations in the Rayleigh-Bénard problem
- Publisher Summary
- 10.1 Experimental techniques
- 10.2 Nonequilibrium light-scattering experiments in one-component fluids
- 10.3 Shadowgraph experiments in one-component fluids
- 10.4 Light scattering in binary systems
- 10.5 Shadowgraphy in binary mixtures

- Chapter 11: Other nonequilibrium fluctuations
- Publisher Summary
- 11.1 Nonequilibrium fluctuations in isothermal one-component fluids under shear
- 11.2 Nonequilibrium interface fluctuations
- 11.3 Nonequilibrium fluctuations in nematic liquid crystals
- 11.4 Concentration fluctuations in reaction-diffusion problems

- Chapter 12: Epilogue
- Publisher Summary

- Bibliography
- List of symbols and corresponding SI units
- List of abbreviations
- Subject index

## Details

- No. of pages:
- 320

- Language:
- English

- Copyright:
- © Elsevier Science 2006

- Published:
- 19th April 2006

- Imprint:
- Elsevier Science

- eBook ISBN:
- 9780080459431

- Paperback ISBN:
- 9780444515155

## About the Author

### Jose Ortiz de Zarate

José Maria Ortiz de Zárate received a Ph.D. from the Universidad Complutense in 1991. In 1994 and 1997 he worked as a postdoctoral researcher at the University of Maryland. Currently he is a faculty member in the Applied Physics Department of the Universidad Complutense. His research interests cover both experimental and theoretical topics in thermal physics of nonequilibrium states.

### Affiliations and Expertise

Universidad Complutense, Madrid, Spain

### Jan Sengers

Jan V. Sengers received a Ph.D. from the University of Amsterdam in 1962. In 1963 he joined the National Bureau of Standards in the U.S. and in 1968 he became a faculty member at the University of Maryland, College Park, MD. Sengers and his co-workers have made extensive theoretical and experimental studies in the areas of critical fluctuations and of nonequilibrium fluctuations in fluids and fluid mixtures

### Affiliations and Expertise

University of Maryland, College Park, U.S.A.