(379f) Multicomponent Maxwell-Stefan Diffusivities At Infinite Dilution

Diffusion plays a crucial role in (bio)chemical processes. It is
usually difficult to obtain Maxwell-Stefan diffusivities from
experiments as well as molecular simulation. Therefore, predictive
models based on easily measurable quantities are highly desired. The
Vignes equation is commonly used to describe the concentration
dependence of Maxwell-Stefan diffusivities. In mixtures containing at
least three components, the generalized Vignes equation requires the
value of the quantity D_ij^x_k->1 , which describes the friction between
components i and j when both are infinitely diluted in component
k. Over the past decades, several empirical models were proposed for
estimating this quantity from binary diffusion data, and all of these are lacking a sound
theoretical basis [1]. Here, we show that D_ij^x_k->1 actually exists, i.e. its value
does not depend on the molar ratio x_i/x_j, and we derive an analytical
expression for D_ij^x_k->1 based on the linear response theory and the Onsager
relations [2]. We find that D_ij^x_k->1 can be expressed in terms of
self-diffusivities and integrals over velocity cross-correlation
functions. By neglecting the latter terms, we obtain a convenient
predictive model for D_ij^x_k->1 in terms of self-diffusivities.

Molecular Dynamics simulations are used to validate the assumptions
made in this model. The following test systems are considered: a
ternary system consisting of particles interacting using
Weeks-Chandler-Andersen (WCA) interactions and the ternary systems
n-hexane-cyclohexane-toluene and ethanol-methanol-water. Our results
show that: (1) for the WCA system as well as the system
n-hexane-cyclohexane-toluene, neglecting the integrals over velocity
cross-correlation functions results in accurate predictions for
D_ij^x_k->1; (2) for the WCA system, our model prediction is superior
compared to the existing models for D_ij^x_k->1; (3) in the
ethanol-methanol-water system, the integrals over velocity
cross-correlation functions cannot be neglected due to the presence of
hydrogen bonds. Models for predicting D_ij^x_k->1 in this system will
require detailed information on the collective motion of molecules;
(4) our model provides an explanation why the Maxwell-Stefan
diffusivity between adsorbed components in a porous material is
usually very large.

References

[1] X. Liu, T.J.H. Vlugt, A. Bardow, Fluid Phase Equilibria,
    (2011), 301, 110-117.

[2] X. Liu, A. Bardow, T.J.H. Vlugt, Ind. Eng. Chem. Res., (2011), in press.