Diffusion Coefficients of a Highly Nonideal Ternary Liquid Mixture: Cyclohexane–Toluene–Methanol

Diffusivity of CO2 in H2O: A Review of Experimental Studies and Molecular Simulations in the Bulk and in Confinement

An in-depth review of the available experimental and molecular simulation studies of CO2 diffusion in H2O, which is a central property in important industrial and environmental processes, such as carbon capture and storage, enhanced oil recovery, and in the food industry is presented. The cases of both bulk and confined systems are covered. The experimental and molecular simulation data gathered are analyzed, and simple and computationally efficient correlations are devised. These correlations are applicable to conditions from 273 K and 0.1 MPa up to 473 K and 45 MPa. The available experimental data for diffusion coefficients of CO2 in brines are also collected, and their dependency on temperature, pressure, and salinity is examined in detail. Other engineering models and correlations reported in literature are also presented. The review of the simulation studies focuses on the force field combinations, the data for diffusivities at low and high pressures, finite-size effects, and the correlations developed based on the Molecular Dynamics data. Regarding the confined systems, we review the main methods to measure and compute the diffusivity of confined CO2 and discuss the main natural and artificial confining media (i.e., smectites, calcites, silica, MOFs, and carbon materials). Detailed discussion is provided regarding the driving force for diffusion of CO2 and H2O under confinement, and on the role of effects such as H2O adsorption on hydrophilic confining media on the diffusivity of CO2. Finally, an outlook of future research paths for advancing the field of CO2 diffusivity in H2O at the bulk phase and in confinement is laid out.

A ternary mixture at the border of Soret separation stability

Ternary mixtures with the Soret effect are prone to triple-diffusive convection in a thermal field. The Soret coefficients of the toluene-methanol-cyclohexane mixture, measured in microgravity at a given composition [0.62-0.31-0.07] in mass fractions, showed that the net separation ratio, Ψ, the parameter responsible for the hydrodynamic stability in a gravity field is close to zero. Furthermore, the large cross-diffusion of toluene leads to a curious situation: the Soret coefficient S_T1 is positive while the thermodiffusion coefficient D_T1 is negative. The behavior of this ternary mixture on the border of stability, when Ψ is slightly negative or positive, is examined experimentally and numerically. The mixture is placed in an elongated cell between the differently heated walls. Depending on Ψ and the initial temperature of the liquid (mean temperature, linear profile or cold one), the evolution of concentration patterns are classified by four regimes. We observe the emergence of motionless, metastable, and convective patterns. In the case of Ψ > 0, it was found that cross-diffusion fluxes cause a temporarily unstable density pattern. The initially cold mixture at either Ψ sign shows dissimilar Soret separation in the upper and lower parts of the cell. It leads to the formation of a long-lived inverse density gradient at the upper part of the cell, which finally results in a motionless (Ψ > 0) or convective (Ψ < 0) pattern.

Generalized Form for Finite-Size Corrections in Mutual Diffusion Coefficients of Multicomponent Mixtures Obtained from Equilibrium Molecular Dynamics Simulation

The system-size dependence of computed mutual diffusion coefficients of multicomponent mixtures is investigated, and a generalized correction term is derived. The generalized finite-size correction term was validated for the ternary molecular mixture chloroform/acetone/methanol as well as 28 ternary LJ systems. It is shown that only the diagonal elements of the Fick matrix show system-size dependency. The finite-size effects of these elements can be corrected by adding the term derived by Yeh and Hummer (J. Phys. Chem. B2004, 108, 15873–15879). By performing an eigenvalue analysis of the finite-size effects of the matrix of Fick diffusivities we show that the eigenvector matrix of Fick diffusivities does not depend on the size of the simulation box. Only eigenvalues, which describe the speed of diffusion, depend on the size of the system. An analytic relation for finite-size effects of the matrix of Maxwell–Stefan diffusivities was developed. All Maxwell–Stefan diffusivities depend on the system size, and the required correction depends on the matrix of thermodynamic factors.

Multicomponent mutual diffusion in the warm, dense matter regime

We present the formulation, simulations, and results for multicomponent mutual diffusion coefficients in the warm, dense matter regime. While binary mixtures have received considerable attention for mass transport, far fewer studies have addressed ternary and more complex systems. We therefore explicitly examine ternary systems utilizing the Maxwell-Stefan formulation that relates diffusion to gradients in the chemical potential. Onsager coefficients then connect the macroscopic diffusion to microscopic particle motions, evinced in trajectories characterized by positions and velocities, through various autocorrelation functions (ACFs). These trajectories are generated by molecular dynamics (MD) simulations either through the Born-Oppenheimer approximation, which treats the ions classically and the electrons quantum-mechanically by an orbital-free density-functional theory, or through a classical MD approach with Yukawa pair-potentials, whose effective ionizations and electron screening length derive from quantal considerations. We employ the reference-mean form of the ACFs and determine the center-of-mass coefficients through a simple reference-frame-dependent similarity transformation. The Onsager terms in turn determine the mutual diffusion coefficients. We examine a representative sample of ternary mixtures as a function of density and temperature from those with only light elements (D-Li-C, D-Li-Al) to those with highly asymmetric mass components (D-Li-Cu, D-Li-Ag, H-C-Ag). We also follow trends in the diffusion as a function of number concentration and evaluated the efficacy of various approximations such as the Darken approximation.

Preliminary analysis of Diffusion Coefficient Measurements in ternary mIXtures 4 (DCMIX4) experiment on board the International Space Station

In the frame of the Diffusion Coefficient Measurements in ternary mIXtures 4 (DCMIX4) project the thermodiffusion experiments were conducted on the International Space Station (ISS) in the Selectable Optical Diagnostics Instrument (SODI) which is on orbit since 2009. We describe the results of the preliminary analysis of images downloaded during the execution of DCMIX4 in order to check the quality of the running experiments and, if needed, adjust the experiment parameters for the following runs. The quick analysis of raw data showed that they are meaningful and will allow to obtain the transport coefficients of examined ternary and binary mixtures.

Nonlinear regimes of Soret-driven convection of ternary fluid with fixed vertical heat flux at the boundaries

Nonlinear regimes of the Soret-induced convection of a ternary mixture in a rectangular cavity with the vertical heat flux at the boundaries are studied numerically. Linear stability analysis performed earlier for a plane horizontal layer has shown that in a wide range of parameters the longwave instability is dominant. Nonlinear calculations performed in the present work for the parameter ranges where the monotonic longwave instability is dominant according to the linear stability analysis, show that at large supercriticalities the multi-vortex stationary flows could be realized. With the decrease of absolute value of the Rayleigh number Ra the series of flow structure transformations takes place. This transformation is accompanied by the decrease of a number of the vortices such that near the threshold the flow becomes two-vortex, i.e. the flow with maximum possible wavelength (minimum possible wave number) is realized. Thus, the nonlinear calculations confirm the conclusions of the linear stability analysis that the longwave instability is dominant. For the parameter ranges where according to the linear stability analysis the oscillatory longwave instability is dominant, the nonlinear calculations show that at small values of the net separation ratio the oscillatory regimes could be observed just in a narrow range of Ra close to the convection threshold and with the growth of net separation ratio the range of Ra where they can be observed is extended.