Hydrodynamic Fluctuations in Fluids and Fluid Mixtures

Hydrodynamic Fluctuations in Fluids and Fluid Mixtures

1st Edition - April 19, 2006

Write a review

  • Authors: Jose Ortiz de Zarate, Jan Sengers
  • eBook ISBN: 9780080459431

Purchase options

Purchase options
DRM-free (EPub, PDF, Mobi)
Sales tax will be calculated at check-out

Institutional Subscription

Free Global Shipping
No minimum order


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.

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


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

Product details

  • No. of pages: 320
  • Language: English
  • Copyright: © Elsevier Science 2006
  • Published: April 19, 2006
  • Imprint: Elsevier Science
  • eBook ISBN: 9780080459431

About the Authors

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.

Ratings and Reviews

Write a review

There are currently no reviews for "Hydrodynamic Fluctuations in Fluids and Fluid Mixtures"