Diffusion Coefficients in Multicomponent Mixtures

Diffusion is the process of relative motion of different components in a mixture. Diffusion mass transfer commonly appears in various industrial processes, including the processes of chemical and petroleum engineering, as well as natural processes related to ecological applications. Knowledge of diffusion coefficients is important for proper description of such processes. Diffusion is normally a slow process and is a rate determining factor in many cases of mass transfer. The hydrodynamic theory of diffusion mass transfer is well developed. However there is no rigorous theory for estimation of the constituting parameters in this theory, the diffusion coefficients. For binary liquid mixtures, extensive databases of experimental values of diffusion coefficients are available. A number of models and correlations for their evaluation is developed. Since these models and correlations are built on empirical or semi-empirical grounds, their predictive capacity is limited. This is a strong limitation, especially because of the limited amount of experimental data available for verification of the models. Lack of rigorous physical theory for diffusion coefficients in liquids and a scarce amount of experimental data for multicomponent mixtures makes it difficult to predict the values of binary diffusion coefficients, and impossible to determine the values of the multicomponent diffusion coefficients outside the ranges of the experimental data available. In the present work, an extensive overview of the mass transfer theory and existing methods for estimation of diffusion coefficients is presented. A large number of experimental data for diffusion coefficients in binary and ternary mixtures is collected, and the most widely used experimental methods are analyzed. Existing models for the diffusion coefficients are also analyzed in detail. It is shown that the existing situation with regard to estimation of the diffusion coefficients requires further development of the theory and a search for more theoretically grounded approaches. Recent developments of the fluctuation theory for diffusion coefficients may provide a rigorous theoretical framework for modeling the diffusion coefficients. The fluctuation theory (FT) for diffusion coefficients is based on the principles of the general statistical fluctuation theory and non-equilibrium thermodynamics, and contains no model assumptions. An expression for the matrix of diffusion coefficients, obtained in the framework of the FT approach, contains several contributions responsible for different physical mechanisms forming these coefficients. Separation of the thermodynamic, kinetic and resistance factors, contributing to the matrix of diffusion coefficients, makes it possible to obtain a fundamental and physically interpretable description of the diffusion coefficients. The thermodynamic contribution is evaluated on the basis of an appropriate thermodynamic model (equation of state) for the mixture, but, unlike many previous approaches, it is not related to a specific model. The resistance contribution depends on the newly introduced parameters, the penetration lengths. Choice of a specific expression for the penetration lengths may be considered as development of a specific model in the framework of the FT approach. The present study has aimed at developing a specific, practically applicable approach to modeling diffusion coefficients in the framework of the fluctuation theory. Two different ways for modeling the penetration lengths (and correspondingly the diffusion coefficients) are considered. The first way is based on the phenomenological considerations and is focused on relating the penetration lengths to the physical properties of the components in the mixture. The particular expressions for the penetration lengths are adjusted to a large number of the experimentally measured diffusion coefficients in binary liquid mixtures. Excellent description of the experimental binary diffusion coefficients over wide temperature and concentration range is obtained. The influence of the choice of a thermodynamic model, used for estimation of thermodynamic contribution, is analyzed. A clear physical meaning of different parameters entering the penetration lengths is demonstrated. Some of these parameters (the so-called penetration volumes) are correlated with the parameters of the equations of state for individual components. The second way is based on molecular dynamics (MD) simulations, which are used to estimate the penetration lengths. A combination of the molecular dynamics and the FT theory creates a new, “mixed” approach to prediction of the diffusion coefficients. While the thermodynamic and kinetic factors are found from thermodynamic modeling, the resistance factor is estimated on the basis of MD simulations. It is shown that penetration lengths, obtained in the framework of the thermodynamic modeling, agree very well with the penetration lengths obtained by MD simulations. The prediction capabilities of both proposed approaches are discussed. It is shown that objective physical reasons make it difficult to make the phenomenological approach fully predictive (at least with a reasonable degree of accuracy). This is related to the high sensitivity of the transport properties, like diffusion coefficients, to the volumetric properties in the liquid state. In the final chapter of the thesis, a procedure for verification of the experimental diffusion coefficients in multicomponent mixtures is developed. The procedure is based on the utilization of the Onsager reciprocal relations, which impose the symmetry of the phenomenological coefficients in multicomponent mixtures. The four experimentally measured Fick diffusion coefficients in ternary mixtures may be reduced to the Onsager phenomenological coefficients by means of thermodynamic transformations. Verification of the experimentally measured diffusion coefficients makes it possible to evaluate both the quality of experimental information and applicability of the thermodynamic models to the modeling of diffusion coefficients.