Static versus dynamic analysis of the influence of gravity on concentration non-equilibrium fluctuations

In a binary fluid mixture subject to gravity and a stabilizing concentration gradient, concentration non-equilibrium fluctuations are long-ranged. While the gradient leads to an enhancement of the respective equilibrium fluctuations, the effect of gravity is a damping of fluctuations larger than a “characteristic” size. This damping is visible both in the fluctuation power spectrum probed by static and the temporal correlation function probed by dynamic light scattering. One aspect of the “characteristic” size can be appreciated by the dynamic analysis; in fact at the corresponding “characteristic” wave vector q * one can observe a maximum of the fluctuation time constant indicating the more persistent fluctuation of the system. Also in the static analysis a “characteristic” size can be extracted from the crossover wave vector. According to common theoretical concepts, the result should be the same in both cases. In the present work we provide evidence for a systematic difference in the experimentally observed “characteristic” size as obtained by static and dynamic measurements. Our observation thus points out the need for a more refined theory of non-equilibrium concentration fluctuations

Slowing-down of non-equilibrium concentration fluctuations in confinement

Fluctuations in a fluid are strongly affected by the presence of a macroscopic gradient making them long-ranged and enhancing their amplitude. While small-scale fluctuations exhibit diffusive lifetimes, larger-scale fluctuations live shorter because of gravity, as theoretically and experimentally well-known. We explore here fluctuations of even larger size, comparable to the extent of the system in the direction of the gradient, and find experimental evidence of a dramatic slowing-down in their dynamics. We recover diffusive behaviour for these strongly-confined fluctuations, but with a diffusion coefficient that depends on the solutal Rayleigh number. Results from dynamic shadowgraph experiments are complemented by theoretical calculations and numerical simulations based on fluctuating hydrodynamics, and excellent agreement is found. The study of the dynamics of non-equilibrium fluctuations allows to probe and measure the competition of physical processes such as diffusion, buoyancy and confinement.Comment: Includes see Supplementary Material. Submitted to PR

Static versus dynamic analysis of the influence of gravity on concentration non-equilibrium fluctuations

Abstract.: In a binary fluid mixture subject to gravity and a stabilizing concentration gradient, concentration non-equilibrium fluctuations are long-ranged. While the gradient leads to an enhancement of the respective equilibrium fluctuations, the effect of gravity is a damping of fluctuations larger than a "characteristic” size. This damping is visible both in the fluctuation power spectrum probed by static and the temporal correlation function probed by dynamic light scattering. One aspect of the "characteristic” size can be appreciated by the dynamic analysis; in fact at the corresponding "characteristic” wave vector q * one can observe a maximum of the fluctuation time constant indicating the more persistent fluctuation of the system. Also in the static analysis a "characteristic” size can be extracted from the crossover wave vector. According to common theoretical concepts, the result should be the same in both cases. In the present work we provide evidence for a systematic difference in the experimentally observed "characteristic” size as obtained by static and dynamic measurements. Our observation thus points out the need for a more refined theory of non-equilibrium concentration fluctuations. Graphical abstract

Confinement effect on the dynamics of non-equilibrium concentration fluctuations far from the onset of convection

In a recent letter (C. Giraudet et al., EPL 111, 60013 (2015)) we reported preliminary data showing evidence of a slowing-down of non-equilibrium fluctuations of the concentration in thermodiffusion experiments on a binary mixture of miscible fluids. The reason for this slowing-down was attributed to the effect of confinement. Such tentative explanation is here experimentally corroborated by new measurements and theoretically substantiated by studying analytically and numerically the relevant fluctuating hydrodynamics equations. In the new experiments presented here, the magnitude of the temperature gradient is changed, confirming that the system is controlled solely by the solutal Rayleigh number, and that the slowing-down is dominated by a combined effect of the driving force of buoyancy, the dissipating force of diffusion and the confinement provided by the vertical extension of the sample cell. Moreover, a compact phenomenological interpolating formula is proposed for easy analysis of experimental results

Thermodiffusion of the tetrahydronaphthalene and dodecane mixture under high pressure and in porous medium

A thermodiffusion cell is used in order to perform Soret experiments on binary mixtures at high pressure and in the presence of a porous medium. The cell is validated at atmospheric pressure with toluene/hexane and the tetrahydronaphthalene/dodecane mixtures. The mass separation follows a diffusive behaviour when the cell is filled with a porous medium. At least three times the relaxation time is needed to have a good estimation of the Soret coefficients. From the transient state of the mass separation and using accepted values of the diffusion coefficient, the tortuosity of the porous medium was evaluated, too. Finally, experiments at high pressure were performed with the tetrahydronaphthalene/dodecane system. In these experiments, decreases of the Soret coefficient and of the tortuosity of the porous medium were measured as a function of the pressure

Concentration dependent refractive index of a binary mixture at high pressure

In the present work binary mixtures of varying concentrations of two miscible hydrocarbons, 1,2,3,4-tetrahydronaphtalene (THN) and n-dodecane (C12), are subjected to increasing pressure up to 50 MPa in order to investigate the dependence of the so-called concentration contrast factor (CF), i.e., (∂n/∂c)p, T, on pressure level. The refractive index is measured by means of a Mach-Zehnder interferometer. The setup and experimental procedure are validated with different pure fluids in the same pressure range. The refractive index of the THN-C12 mixture is found to vary both over pressure and concentration, and the concentration CF is found to exponentially decrease as the pressure is increased. The measured values of the refractive index and the concentration CFs are compared with values obtained by two different theoretical predictions, the well-known Lorentz-Lorenz formula and an alternative one proposed by Looyenga. While the measured refractive indices agree very well with predictions given by Looyenga, the measured concentration CFs show deviations from the latter of the order of 6% and more than the double from the Lorentz-Lorenz prediction

Propagating modes in a binary liquid mixture under thermal stress

Nonequilibrium temperature and concentration fluctuations inside a binary liquid mixture under the action of a temperature gradient relax back to equilibrium either due to conduction and diffusion at large wave numbers, or due to the quenching determined by gravity at small wave numbers. We investigate the dynamics of nonequilibrium fluctuations in a binary liquid mixture of polystyrene and toluene heated from above under stationary conditions in a thermodiffusion experiment. We show that the strong gravitational stabilization at small wave numbers determines the appearance of propagating modes of nonequilibrium fluctuations as detected through the structure function of shadowgraph images. The propagating modes are the combined effect of temperature and velocity nonequilibrium fluctuations induced by the buoyancy force. The experimental results are in good agreement with a fluctuating hydrodynamics theroretical model including the coupling of fluctuations of velocity, temperature and concentration

SCCO: Thermodiffusion for the Oil and Gas Industry

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