(414l) A Liquid Maxwell-Stefan Diffusion Coefficient Prediction Model Derived from Entropy Generation Minimization Principle

Diffusion plays an important role in all kinds of chemical
processes, e.g., diffusion within fluid phases, across phase interfaces, within
gels, porous catalysts and adsorbents, and across porous membranes. In all the
cases, diffusion coefficient is a fundamental parameter for mass transfer
process design and performance evaluations. Traditionally, mass transfer
process can be modeled by Fick's law of diffusion. However, the generalized
Fick's law of diffusion is valid for ideal mixtures. In many highly non-ideal
systems, it is complicated or even unpredictable to describe the diffusion
process. Maxwell-Stefan (MS) equation, describing the driving force for
diffusion in the terms of a gradient of chemical potential which is more correct
from a thermodynamic perspective, has been used in many mass transfer
processes. MS diffusion coefficient cannot be directly obtained from
experiments as chemical potential gradients cannot be measured directly, and
then there has been a need to develop models to predict the MS diffusion
coefficient.

In this work, the entropy generation minimum principle is used to
develop the MS diffusion coefficient model. This entropy generation is employed
as the minimum objective function. There is also a constraint about the mass
conservation of species in a steady-state and no bulk flow contribution
diffusion process. Through calculus of variation and solving of ordinary
differential equation, the expression of the MS diffusion coefficient is
derived in a form of the general
expression of the Erying¡¯s equation.

According to the
lattice theory and the partition function of a liquid mixture, we derived the molar excess internal energy as new
correction term is used to modify the linear mixing rule. And the bulk fraction
is replaced by the local surface area fraction due to the directly relative to
local surface area fractions rather than the bulk fractions. The proposed model
is as following:

Fick¡¯s diffusion coefficient is then calculated by using
thermodynamic correction factor derived from UNIQUAC equation. To validate the
proposed model and compare with other available models, Fick diffusion
coefficients of four different binary liquid mixtures including acetone-water,
ethanol-water, acetone-carbon tetrachloride, and ethanol-benzene, are
experimentally measured by employing digital holographic interferometry
technique (Fig. 1). The predictive results of the proposed model are shown in
Fig. 2 to Fig. 5.

Fig. 1 Optical diagram of digital holographic interferometer: 1,
semi-conductor laser source; 2, attenuator; 3, expander lens; 4, spatial
filter; 5, adjustable diaphragm; 6, collimation lens; 7, spectroscope; 8,
mirrors; 9, diffusion cell; 10, CCD camera; 11, PC.

Fig.
2 Predicted MS diffusion coefficient, Đ , predicted
Fick diffusion coefficient, D_pre and experimental Fick diffusion
coefficient, D_exp,
in acetone-water system at 25¡æ

Fig.
3 Predicted MS diffusion coefficient, Đ , predicted
Fick diffusion coefficient, D_pre and experimental Fick diffusion
coefficient, D_exp,
in ethanol-water system at 25¡æ

Fig.
4 Predicted MS diffusion coefficient, Đ , predicted
Fick diffusion coefficient, D_pre and experimental Fick diffusion
coefficient, D_exp,
in acetone-carbon tetrachloride system at 25¡æ

Fig.
5 Predicted MS diffusion coefficient, Đ , predicted
Fick diffusion coefficient, D_pre and experimental Fick diffusion
coefficient, D_exp,
in ethanol-benzene system at 25¡æ