Thermomechanical Point of View of the Effect of Pressure and Free Volume on the Molecular Diffusion Coefficients

The effects of high pressure and
free volume on the mutual-, tracer-,
and self-diffusion coefficients of pure components and binary mixtures
of light gases and hydrocarbons (both pure and mixed) are addressed
from the continuum mechanical and classical thermodynamics standpoint.
First, an analogy between the friction between two macroscopic bodies
and the friction at microscopic level is proposed so that the pressure
is incorporated into constitutive equations for diffusion from the
continuum mechanical theory. Then, by making use of the local equilibrium
assumption, the fugacity coefficient and the compressibility factor,
defined at equilibrium, are introduced into such modified constitutive
equations. The suggested method allows us to derive some expressions
for diffusion coefficients found in the open literature. Besides,
it was found that the calculated diffusion coefficients are in agreement
with experiments for free volume fractions larger than 0.2 approximately.
Hence, a wider range was obtained by incorporating not only the pressure
but also the free volume fraction into the constitutive equations.
The final expressions for estimating the diffusion coefficients are
in better agreement with experiments than some correlations from the
open literature for the entire range of free volume fractions, which
are estimated by using parameters from the PC-SAFT and the PR equations
of state.