Diffusion Coefficients In Multicomponent Mixtures Research Articles

Experimental Determination of H2 and CO Diffusion Coefficients in a Wax Mixture Confined in a Porous Titania Catalyst Support.

The ability to measure and predict molecular diffusion coefficients in multicomponent mixtures is not only of fundamental scientific interest but also of significant relevance in understanding how catalytic processes proceed. In the present work, the direct measurement of the molecular diffusion of H2 and CO gas-phase species diffusing in n-alkane mixtures using pulsed-field gradient (PFG) nuclear magnetic resonance (NMR) methods is reported. The work is of direct relevance to Fischer-Tropsch (FT) catalysis, with the measurements being made of the gas-wax system with the wax in both the bulk liquid state and when confined within a titania catalyst support, at temperatures and pressures typical of low-temperature FT synthesis. Molecular diffusion coefficients of H2 and CO within wax-saturated porous titania in the range (1.00-2.43) × 10-8 and (6.44-8.50) × 10-9 m2 s-1, respectively, were measured in the temperature range of 140-240 and 200-240 °C for H2 and CO, respectively, at a pressure of 40 bar. The wax mixture was typical of a wax produced during FT catalysis and had a molar average carbon number of 36. It is shown that the hydrogen diffusion coefficient within this wax mixture is consistent, to within experimental error, with the hydrogen diffusion coefficient measured in pure single-component n-hexatriacontane (n-C36) wax; this result held with the waxes in the bulk liquid state and when confined within the porous titania. The tortuosity of the porous titania was also measured using PFG NMR and found to be 1.77; this value is independent of temperature. The ability of existing correlations to predict these experimentally determined data was then critically evaluated. Although the Wilke-Chang correlation was found to underestimate the molecular diffusion coefficients of both H2 and CO diffusing in the wax in both the bulk state and when confined within the porous titania, parameterized correlations based on the rough hard sphere model, having accounted for the experimentally determined tortuosity factor, predicted the H2 and CO diffusion within bulk and confined wax to within 3%.

Predictive Darken Equation for Maxwell-Stefan Diffusivities in Multicomponent Mixtures

This Article presents the derivation and validation of a rigorous model for the prediction of multicomponent Maxwell-Stefan (MS) diffusion coefficients. The MS theory provides a sound framework for modeling mass transport in gases and liquids. Unfortunately, MS diffusivities are concentration dependent, and this needs to be taken into account in practical applications. There is therefore a considerable interest in models describing the concentration dependence of MS diffusivities. While current practice employs empirical models for this purpose, recent work on molecular simulations favor the physically based Darken equation. The Darken equation, however, is limited to binary mixtures and is not predictive. In this study, a multicomponent Darken model for MS diffusivities is derived from linear response theory and the Onsager relations. In addition, a predictive model for the required self-diffusivities in the mixture is proposed, leading to the predictive Darken-LBV model. We compare our novel model to the existing generalized Vignes equation and the generalized Darken equation using molecular dynamics (MD) simulation. Two systems are considered: (1) ternary and quaternary systems in which particles are interacting using the Weeks-Chandler-Andersen (WCA) potential; (2) the ternary system n-hexane-cyclohexane-toluene. Our results show that, in all studied systems, the novel predictive Darken-LBV equation describes the concentration dependence better than the existing models. The physically based Darken-LBV model provides a sound and robust framework for prediction of MS diffusion coefficients in multicomponent mixtures.

On Measurement of Molecular and Thermal Diffusion Coefficients in Multicomponent Mixtures

We have developed the theory for using the deflection of laser beams of various wavelengths to determine molecular and thermal diffusion coefficients in multicomponent mixtures. In the past, simultaneous determination of molecular and thermal diffusion coefficients have only been achieved for binaries. Our procedure is faster and more accurate than the current techniques to determine molecular diffusion coefficients. The analysis for an N-component mixture requires deflections from (N - 1) beams of different wavelengths. We show in an example that the molecular and thermal diffusion coefficients can be determined reliably in a ternary mixture.

Verifying reciprocal relations for experimental diffusion coefficients in multicomponent mixtures

The goal of the present study is to verify the agreement of the available data on diffusion in ternary mixtures with the theoretical requirement of linear non-equilibrium thermodynamics consisting in symmetry of the matrix of the phenomenological coefficients. A common set of measured diffusion coefficients for a three-component mixture consists of four Fickian diffusion coefficients, each being reported separately. However, the Onsager theory predicts the existence of only three independent coefficients, as one of them disappears due to the symmetry requirement. Re-calculation of the Fickian diffusion coefficients into Onsager coefficients for a non-ideal mixture involves derivatives of the chemical potentials and, thus, should be based on a certain thermodynamic model (cubic equation of state (EoS), an activity coefficient model, etc.). Transformation of the Fickian diffusion coefficients into Onsager coefficients and a subsequent symmetry check make it possible to evaluate different thermodynamic models with regard to their possibility of being used for prediction of the transport properties. We performed several checks of this kind for ternary mixtures of hydrocarbons and alcohols, where extended sets of experimental data and reliable thermodynamic models were available. The sensitivity of the symmetry property to different thermodynamic parameters of the models was also checked.

Evaluation of diffusion coefficients in multicomponent mixtures by means of the fluctuation theory

We derive general expressions for diffusion coefficients in multicomponent non-ideal gas or liquid mixtures. The derivation is based on the general statistical theory of fluctuations around an equilibrium state. The matrix of diffusion coefficients is expressed in terms of the equilibrium thermodynamic characteristics of the mixture (such as molar densities and internal energy), as well as in terms of the newly introduced parameters, the penetration lengths. This result serves to reduce the problem of determining the diffusion coefficients to a smaller number of physically meaningful characteristics. We demonstrate on several examples that the developed theory is in agreement with the established experimental facts and dependencies for the diffusion coefficients.