Thermodiffusion in multicomponent n-alkane mixtures

Unraveling dispersion and buoyancy dynamics around radial A + B → C reaction fronts: microgravity experiments and numerical simulations

Radial Reaction-Diffusion-Advection (RDA) fronts for A + B → C reactions find wide applications in many natural and technological processes. In liquid solutions, their dynamics can be perturbed by buoyancy-driven convection due to concentration gradients across the front. In this context, we conducted microgravity experiments aboard a sounding rocket, in order to disentangle dispersion and buoyancy effects in such fronts. We studied experimentally the dynamics due to the radial injection of A in B at a constant flow rate, in absence of gravity. We compared the obtained results with numerical simulations using either radial one- (1D) or two-dimensional (2D) models. We showed that gravitational acceleration significantly distorts the RDA dynamics on ground, even if the vertical dimension of the reactor and density gradients are small. We further quantified the importance of such buoyant phenomena. Finally, we showed that 1D numerical models with radial symmetry fail to predict the dynamics of RDA fronts in thicker geometries, while 2D radial models are necessary to accurately describe RDA dynamics where Taylor-Aris dispersion is significant.

Diffusion in liquid mixtures

The understanding of transport and mixing in fluids in the presence and in the absence of external fields and reactions represents a challenging topic of strategic relevance for space exploration. Indeed, mixing and transport of components in a fluid are especially important during long-term space missions where fuels, food and other materials, needed for the sustainability of long space travels, must be processed under microgravity conditions. So far, the processes of transport and mixing have been investigated mainly at the macroscopic and microscopic scale. Their investigation at the mesoscopic scale is becoming increasingly important for the understanding of mass transfer in confined systems, such as porous media, biological systems and microfluidic systems. Microgravity conditions will provide the opportunity to analyze the effect of external fields and reactions on optimizing mixing and transport in the absence of the convective flows induced by buoyancy on Earth. This would be of great practical applicative relevance to handle complex fluids under microgravity conditions for the processing of materials in space.

Predicting thermodiffusion in simple binary fluid mixtures

The predictive capabilities of some existing theoretical models to quantify thermodiffusion have been investigated in this work. To do so, the tests have been performed on two model fluids, the hard-sphere and the Lennard-Jones (including spheres and dimers) ones, exploring different mixtures and thermodynamic conditions thanks to extensive molecular simulations. It has been confirmed that the thermal diffusion factor should be expressed as the sum of one term related to the isotope effect and one term related to the "chemical" effects and that a kinetic term is required to quantify thermodiffusion from the gas state to the liquid state. In addition, regarding the isotope effects, it has been obtained that none of the available theoretical models are able to yield a reasonable prediction relatively to the molecular simulations results and that the moment of inertia contribution is one order of magnitude smaller than the mass contribution in the liquid state. Finally, concerning the chemical effects, it has been shown the Shukla and Firoozabadi model, complemented with a kinetic term, is probably the most reasonable option to estimate the chemical contribution to the thermal diffusion factor, even if it fails in capturing the effect of the asymmetry in size and in shape between the species. Overall, this works confirms that there is still a lack of a generic model able to predict accurately thermal diffusion factors, or equivalently Soret coefficient, in simple binary mixtures from the gas state to the liquid state.

Mass diffusion and Soret coefficient measurements of triethylene glycol/water binary mixtures by dynamic shadowgraphy

The investigation of the transport properties of binary fluid mixtures remains a topic of interest in relation to the more challenging studies of ternary mixtures. In fact, the study of the phase boundary limits of the Gibbs composition triangle can be the initial step for a more complete analysis of ternary mixtures. In this paper, we apply the dynamic shadowgraphy optical technique to study non-equilibrium fluctuations induced by the presence of a gradient of temperature and/or concentration in the triethylene glycol (TEG)/water system. These thermodiffusion and free-diffusion experiments aim at measuring the transport properties of samples of the studied system at different experimental conditions. We scan both the average temperature and the TEG concentration, which allows us investigating both positive and negative thermodiffusive behaviours. The obtained values of mass diffusion coefficient are consistent with data available in the literature in the range of temperature investigated in this study. The mass diffusion coefficient of the sample prepared at 0.7 w/w TEG concentration are characterised by shadowgraphy following the two proposed methods, exhibiting consistent results. An increase of the mass diffusion coefficient as a function of the average temperature is highlighted. On the other hand, the thermodiffusion coefficient appears to be independent of the average temperature of the sample at 0.3 w/w TEG concentration.

Molecular Dynamics Simulation of the Soret Effect on Two Binary Liquid Solutions with Equimolar n-Alkane Mixtures

Molecular dynamics is employed to simulate the Soret effect on two binary liquid solutions with equimolar mixtures: normal pentane (n-pentane, nC-5) and normal heptane (n-heptane, nC-7) molecules plus normal decane (n-decane, nC-10) and normal pentane molecules. Moreover, two coarse-grained force field (the CG-FF) potentials, which may depict inter-/intramolecular interactions fairly well among n-alkane molecules, are developed to fulfill such investigations. In addition, thermal diffusion for the mass fraction of each of these n-alkane molecules is simulated under an effect of a weak thermal gradient (temperature difference) exerting on solution systems from their hot to cold boundary sides. Finally, quantities of the Soret coefficient (SC) for two binary solutions are calculated by means of the developed CG-FF potentials, so as to improve the calculation rationality. As a result, first, it is found that molecules with light molar masses will migrate toward the hot boundary side, while those with heavy molar masses will migrate toward the cold boundary one ; second, the SC quantities indicate that they match relevant experimental determinations fairly well, i.e., trends of these SC quantities show inverse proportionality to the thermal gradient on the systems.

Frame-invariant Fick diffusion matrices of multicomponent fluid mixtures

Extension of a description of mass diffusion in binary fluids based on Fick's law to multicomponent fluids requires introduction of diffusion matrices. A problem is that Fick diffusion matrices commonly adopted for multicomponent fluids depend on the velocity frame of reference. In this paper we show how one can define Fick diffusion matrices for multicomponent fluids that are frame invariant.

Coupled non-equilibrium fluctuations in a polymeric ternary mixture

We investigate by dynamic shadowgraphy the non-equilibrium fluctuations at the steady state of a thermodiffusion experiment in a polymeric ternary mixture of polystyrene-toluene-n-hexane. The structure function of the refractive index reveals the existence of quite different decay times, thus requiring the analysis of a wide range of correlation times. This is related to the simultaneous presence of three distinct decay modes corresponding to (from fastest to slowest) the relaxation of temperature fluctuations, of the concentration fluctuations of the mixed solvent, and of the concentration fluctuations of the polymer in the binary solvent. An investigation of the decay times at the corresponding diffusive regimes provides a measurement of the thermal diffusivity and the two eigenvalues of the mass diffusion matrix of the ternary mixture. Similar experiments were performed in the past but here, to suppress the confinement effect and obtain a more direct comparison with the theory, a thicker sample is studied. Moreover, also a faster camera is used allowing the experimental observation of faster modes, like the propagative ones. The experimental values of the decay times are eventually compared with those predicted by different available theories. Finally, we present a more complete theoretical model to describe the non-equilibrium fluctuations in the bulk of a ternary mixture at the steady state of a thermodiffusion experiment.

European Space Agency experiments on thermodiffusion of fluid mixtures in space

This paper describes the European Space Agency (ESA) experiments devoted to study thermodiffusion of fluid mixtures in microgravity environment, where sedimentation and convection do not affect the mass flow induced by the Soret effect. First, the experiments performed on binary mixtures in the IVIDIL and GRADFLEX experiments are described. Then, further experiments on ternary mixtures and complex fluids performed in DCMIX and planned to be performed in the context of the NEUF-DIX project are presented. Finally, multi-component mixtures studied in the SCCO project are detailed.

Definition of frame-invariant thermodiffusion and Soret coefficients for ternary mixtures

The definitions of thermodiffusion and Soret coefficients for a binary mixture include a concentration prefactor x(1 - x), when mole fraction x is used, or w(1 - w), when mass fraction w is used. In this paper the physical reasons behind this choice are reviewed, emphasizing that the use of these prefactors makes the thermodiffusion and the Soret coefficients invariant upon changing in the concentration representation, using either mole fraction or mass faction. Then, it is shown how this invariance property can be extended to ternary mixtures by using appropriate concentration prefactors in matrix form. The paper is completed with some considerations about alternative definitions of thermodiffusion coefficients, binary limits of the concentration triangle, selection of the dependent concentration in a ternary mixture, use of molar concentrations and, finally, extension to multi-component mixtures.

Composition effect on thermophobicity of ternary mixtures: An enhanced molecular dynamics method

Thermodiffusion or the Ludwig-Soret effect is known as the cross effect between the temperature gradient and induced separation of mixture species in multicomponent mixtures. The performance of the boundary driven non-equilibrium molecular dynamics enhanced heat exchange (eHEX) algorithm was validated by evaluating the sign and magnitude of the thermodiffusion process in methane/n-butane/n-dodecane (nC₁-nC₄-nC₁₂) ternary mixtures. The eHEX algorithm consists of an extended version of the HEX algorithm with an improved energy conservation property. In addition to this, the transferable potentials for phase equilibria-united atom augmented force field was employed in all molecular dynamics (MD) simulations to accurately represent molecular interactions in the fluid. Our newly employed MD algorithm was capable to appropriately reflect the thermophobicity concept and the coupled effect of relative density and mole fraction of the mixture species on the thermodiffusion process. The separation ratio of the ternary mixture for five different compositions (at 333.15 K and 35 MPa) showed good agreement with experimental data and better accuracy in predicting the sign change of the intermediate component (nC₄) as its concentration in the mixture increases, when compared to other MD models.

Thermal Diffusion in Binary Mixtures: Transient Behavior and Transport Coefficients from Equilibrium and Nonequilibrium Molecular Dynamics

Equilibrium and nonequilibrium molecular dynamics simulations are combined to compute the full set of coefficients that appear in the phenomenological equations describing thermal transport in a binary mixture subject to a constant thermal gradient. The Dynamical Non-Equilibrium Molecular Dynamics approach (D-NEMD) is employed to obtain the microscopic time evolution of the density and temperature fields, together with that of the mass and energy fluxes. D-NEMD enables one to study not only the steady state, but also the evolution of the fields during the transient that follows the onset of the thermal gradient, up to the establishment of the steady state. This makes it possible to ensure that the system has indeed reached a stationary condition, and to analyze the transient mechanisms and time scales of the mass and energy transport. A local time averaging procedure is applied to each trajectory contributing to the calculation to improve the signal-to-noise ratio in the estimation of the fluxes and to obtain a clear signal with the, relatively limited, statistics available.