Henri Bataller

A light scattering study of non equilibrium fluctuations in liquid mixtures to measure the Soret and mass diffusion coefficient.

We use dynamic near field scattering to measure the dynamics of concentration non equilibrium fluctuations at the steady-state of Soret separation. The analysis reveals that above a threshold wave vector q(c), the dynamics is governed by diffusion while at smaller wave vectors, gravity dominates. From the measurements, we extract both the mass diffusion and the Soret coefficients. Comparing our results with literature data, we find good agreement confirming that the proposed experimental technique can be considered a sound approach for the study of thermodiffusion processes.

High-pressure mass transport properties measured by dynamic near-field scattering of non-equilibrium fluctuations

High-pressure mass diffusion and Soret coefficients of the equimassic 1,2,3,4-tetrahydronaphthalene and n-dodecane binary mixture are obtained from dynamic light scattering analysis of concentration non-equilibrium fluctuations at the steady state of Soret-driven separation. A high-pressure shadowgraph set-up has been developed to investigate thermodiffusion in free medium from atmospheric pressure up to 20MPa. Results at atmospheric pressure show excellent agreement with benchmark values. High-pressure results for the mass diffusion coefficient confirm theoretical predictions by Leffler-Cullinan relation. Further calculation of the thermodiffusion coefficient allows also comparison with previous experimental results with, again, very good agreement.Graphical abstract

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 predictions.

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.

Measurement of thermodiffusion coefficient of hydrocarbon binary mixtures under pressure with the thermogravitational technique

It was designed and constructed a new thermogravitational column able to operate at high pressures (up to 50 MPa). This new thermogravitational column is of the cylindrical type with closed ends. It is made of stainless steel. The length of the column is 0.5 m and the gap between its two walls is variable. First, the column was validated at atmospheric pressure by means of measurements of the thermodiffusion coefficient of well-known binary mixtures. Then, this new thermogravitational column was used to measure the thermodiffusion coefficient of the binary mixtures 1,2,3,4-tetrahydronaphtalene/isobutylbenzene, 1,2,3,4-tetrahydronaphtalene/n-dodecane, and isobutylbenzene/n-dodecane at high pressures and within the pressure range between 0.1 and 20 MPa at a mean temperature of 25 °C. We have found a linear dependence between the thermodiffusion coefficient and the pressure.

Note: Temperature derivative of the refractive index of binary mixtures measured by using a new thermodiffusion cell

A thermodiffusion cell is developed for performing Soret experiments on binary mixtures at high pressure and in the presence of a porous medium. The cell is validated by performing experiments at atmospheric pressure. The experiments are performed by applying different temperature gradients to binary mixtures in order to determine their thermal contrast factor. These measurements provide a first demonstration of the good reproducibility of this kind of measurements upon calibration.

Non-equilibrium fluctuations induced by the Soret effect in a ternary mixture

We present, based on fluctuating hydrodynamics, the theory of concentration fluctuations in a ternary mixture subjected to a stationary temperature gradient, so that composition gradients are present due to thermal diffusion (Soret effect). We neglect gravity and confinement (boundary conditions) but consider a completely generic diffusion matrix, including cross-diffusion effects. We find, as in the case of binary mixtures, an important non-equilibrium enhancement of the concentration fluctuations, which is proportional to the square of the gradient and inversely proportional to the fourth power of the fluctuations wave number, q−4. The results of this paper are expected to be asymptotically correct for fluctuations of large q, while for shorter q gravity and confinement effects need to be incorporated. Comparison with previous work in the topic is included.Graphical abstract

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

Determination of the Tortuosity of a Porous Medium by Means of A Thermodiffusion Cell

We present a technique for determining the value of the tortuosity of a porous medium by performing a separation experiment in a thermodiffusion cell. A temperature difference is applied to a binary mixture while its refractive index is measured by means of a Mach‐Zehnder interferometry. The refractive index shows a fast change due to the thermal gradient and a slower one due to the separation induced by the Soret effect. Thus we are able to deduce the mass diffusion coefficient of the sample within the porous medium. By knowing the value of the diffusion coefficient in the free medium and the simple relation between the two values D* = D/τ, we can calculate the tortuosity of the porous medium. Experimental trials on two distinct samples show a good agreement within the two measured values, but also that the diffusion in a volume which is partly free and partly filled with a porous medium is not theoretically described by our formula.

Thermodiffusion in multicomponent n -alkane mixtures

Compositional grading within a mixture has a strong impact on the evaluation of the pre-exploitation distribution of hydrocarbons in underground layers and sediments. Thermodiffusion, which leads to a partial diffusive separation of species in a mixture due to the geothermal gradient, is thought to play an important role in determining the distribution of species in a reservoir. However, despite recent progress, thermodiffusion is still difficult to measure and model in multicomponent mixtures. In this work, we report on experimental investigations of the thermodiffusion of multicomponent n-alkane mixtures at pressure above 30 MPa. The experiments have been conducted in space onboard the Shi Jian 10 spacecraft so as to isolate the studied phenomena from convection. For the two exploitable cells, containing a ternary liquid mixture and a condensate gas, measurements have shown that the lightest and heaviest species had a tendency to migrate, relatively to the rest of the species, to the hot and cold region, respectively. These trends have been confirmed by molecular dynamics simulations. The measured condensate gas data have been used to quantify the influence of thermodiffusion on the initial fluid distribution of an idealised one dimension reservoir. The results obtained indicate that thermodiffusion tends to noticeably counteract the influence of gravitational segregation on the vertical distribution of species, which could result in an unstable fluid column. This confirms that, in oil and gas reservoirs, the availability of thermodiffusion data for multicomponent mixtures is crucial for a correct evaluation of the initial state fluid distribution.Microgravity simulators: improving oil field assessmentsTo support oil and gas exploration, researchers sent hydrocarbon mixtures into space to obtain accurate data on how each component behaves. The group—led by Guillaume Galliero from the University of Pau and Pays de l’Adour, France—wanted to study the effect of temperature on the movement of individual hydrocarbons in mixtures under typical reservoir conditions. Eliminating the effects of gravity allowed them to collect more accurate data than has previously been obtained. The team showed that thermodiffusion has a large impact on the distribution of hydrocarbon reservoirs under the ground. They state that thermodiffusion should therefore be considered in computer models that assess analytical data collected at potential underground reservoirs. This would allow oil and gas companies to more accurately predict the suitability of the hydrocarbons at potential drilling sites.