GENERAL RESEARCH
Near-Critical Behavior of Mutual Diffusion Coefficients for Five
Solutes in Supercritical Carbon Dioxide
Xiao-ning Yang, Luiz A. F. Coelho, and Michael A. Matthews
Department of Chemical Engineering, University of South Carolina, Columbia, South Carolina 29208
The Taylor-Aris dispersion technique was employed to measure the binary diffusion coefficients
of five solid solutes (phenanthrene, biphenyl, benzoic acid, 1,4-dichlorobenzene, and phenol) in
supercritical carbon dioxide within the pressure range from 75 to 170 bar at 308.2 K.
Measurements were made at very dilute concentrations, in the vicinity of the pure CO
2
critical
point and also near the solid/supercritical fluid lower critical end point. At 308.2 K (4 K above
the critical temperature of the solvent), decreasing the pressure (density) of the fluid causes the
binary diffusion coefficients to increase until a certain pressure is reached. With further decreases
in pressure, approaching the critical pressure of CO
2
, the diffusion coefficients decrease sharply.
The decrease in diffusion coefficient near the solvent critical point is discussed using the concept
of the solvent density inhomogeneities in supercritical fluids. A crossover theory that considers
both the critical singular contribution and background contribution of transport properties is
used to describe semiquantitatively the observed decrease in the diffusion coefficient.
Introduction
Carbon dioxide is a preferred supercritical fluid (SCF)
solvent due to its low cost, easily accessible critical point,
and environmentally benign nature. The design of SCF
processes involving interfacial mass transfer requires
knowledge of the binary diffusion coefficients. Behavior
of the diffusion coefficient near the solvent critical point
or near a binary mixture critical point may greatly
influence dynamic processes. For example, in particle
formation by rapid expansion or gas antisolvent pro-
cesses, the particle size and morphology are a function
of mass transfer characteristics as well as the specific
process path into the two-phase region. The specific
effect of diffusion coefficient on such processes is un-
known but is thought to be crucial. Theoretically,
diffusion coefficients are of great importance in provid-
ing information regarding specific interactions between
unlike molecules.
Measurement and analysis of diffusion coefficients
very near the solvent critical point is challenging.
1,2
In
general, diffusion coefficients are expected to increase
as the pressure of a fluid is decreased (or equivalently,
as density is decreased). However, near the solvent
critical point the mutual diffusion coefficients decrease
with decreasing pressure.
3-6
Also, for incompressible
mixtures near a liquid-liquid critical (or consulate)
point the mutual diffusion coefficients have been found
to fall toward zero.
7,8
This phenomenon has an impor-
tant bearing on any process operating in this region.
The near-critical behavior has been explained by con-
sidering the chemical potential gradient as the driving
force for diffusional process.
4,5,9
According to this de-
velopment, the determinant of the matrix for the
diffusion coefficients in multicomponent systems tends
toward zero near the critical point.
10
Clifford and
Coleby
11
discussed the decrease in the mutual diffusion
coefficients in the region near the pure solvent critical
point and suggested that the decrease in diffusivity may
not happen at infinite dilution. According to Levelt-
Sengers et al.,
12
it is difficult to see experimentally the
decrease in diffusion coefficients at infinite dilution near
the solvent critical point.
One characteristic of critical behavior is the strong
divergence of the susceptibility for mixtures (compress-
ibility for pure fluids) and the related growth of the
correlation length,
2,9,12
which can be described by means
of scaling laws.
13
However, it should be pointed out that
the validity of the scaling laws is restricted to the region
extremely close to the critical point. In this region very
close to the critical point, the anomalous asymptotic
behavior of transport properties dominates to the extent
that the normal background can be neglected. But it has
become evident that critical fluctuations are actually
present in fluids over a very large range of temperature
and pressure.
14
To account for the effects of critical fluctuations on
transport properties, it is necessary to consider the
nonasymptotic behavior of transport properties includ-
ing the crossover to background (regular) classical
behavior far away from the critical point. Recently, an
advanced treatment of critical phenomena has been
developed for studying transport properties in the
critical region
15-18
based on the mode-coupling theory.
Luettmer-Strathman and Sengers
15
extended the de-
scription of transport properties of binary mixtures into
the crossover region. Kiselev and Kulikov
16
developed
a practical representation of thermodynamic and trans-
port properties in pure and binary mixtures near the
vapor-liquid critical line. However, these studies are
3059 Ind. Eng. Chem. Res. 2000, 39, 3059-3068
10.1021/ie990705d CCC: $19.00 © 2000 American Chemical Society
Published on Web 07/13/2000