Light scattering and shadowgraph measurements of nonequilibrium fluctuations in fluids Jan V. Sengers Institute for Physical Science and Technology University of Maryland, College Park, MD th Statistical Mechanics Meeting Rutgers University, May 6-8, 2012

Outline 1. Introduction: statement of problem 2. Equilibrium fluctuating hydrodynamics 3. Nonequilibrium fluctuating hydrodynamics 4. Light-scattering experiments 5. New shadowgraph experiments: gravity and finite-size effects

THERMAL FLUCTUATIONS IN FLUIDS L T1T1 T2T2 T 1 = T 2

Thermal fluctuations in a temperature gradient T1T1 T2T2 L Rayleigh number: α is thermal expansion coefficient ν is kinematic viscosity a = λ/ρc p is thermal diffusivity T 1 > T 2

T.R. Kirkpatrick, E.G.D. Cohen, and J.R. Dorfman Phys. Rev. Lett. 44, 472 (1980)

Example: stochastic temperature evolution equation (at constant pressure) “Fluctuating” heat equation Linear phenomenological laws are valid only “on average”: Fluctuating Hydrodynamics

Thermal fluctuations in equilibrium Fluctuation-dissipation theorem:

Fluid in temperature gradient Fluctuating heat equation: Fluctuating Navier-Stokes equation at constant pressure: Coupling between heat mode and viscous mode through  T 0

Assumption: local equilibrium for noise correlations

Fluids in a temperature gradient T.R. Kirkpatrick, J.R. Dorfman and E.G.D. Cohen, Phys. Rev. A 26, 995 (1982), D. Ronis and I. Procaccia, Phys. Rev. A 26, 1812 (1982), B.M. Law and J.V. Sengers, J. Stat. Phys. 57, 531 (1989).

Bragg-Williams condition

Toluene q=2255 cm –1,  T=220 K/cm Law, Segrè, Gammon, Sengers, Phys. Rev. A 41, 816 (1990)

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J.M. Ortiz de Zárate and J.V. Sengers Solid curve: R=1700 Dashed curve: R=0 Dotted curve: R=  25,000

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J.Oh, J.M.Ortiz de Zárate, J.V.Sengers, G.Ahlers Phys. Rev. E 69, (2004)

Vailati, Cerbino, Mazzoni, Giglio, Nikolaenko, Takacs, Cannell, Meyer, Smart, Applied Optics 45, 2155 (2006)

C.J. Takacs, A. Vailati, R. Cerbino, S. Mazzoni, M. Giglio, D.S. Cannell PRL 106, (2011)