Handbook of Solvents - George Wypych - ChemTech - Ventech!

1432 Aydin K. Sunol and Sermin G. Sunol
Most of the theoretically based estimation methods for viscosity of dense gases rely on
modified Enskog theory. Corresponding states based methods are also popular but should
be used with care due to their empiric nature.
21.1.2.2.2 Diffusivity
The experimental techniques used to measure the diffusion are based upon chromatographic
methods, 19 NMR (for self-diffusion), and photon correlation spectroscopy. 45
The so called chromatographic method for the measurement of diffusion coefficients,
strictly speaking, is not a chromatographic method since no adsorption/desorption or retention
due to partition in two phases are involved in the method. The experimental system
used is however a chromatograph. Diffusion occurs in an empty, inert column on which the
fluid phase is not supposed to be adsorbed. The fluid, in which the solute diffuses flows,
continuously through the empty column and the solute, which is introduced into the column
at one end, is detected at the other end as effluent concentration.
The theory of diffusion in flowing fluids is first given by Taylor 46 and Aris. 47 According
to Aris, a sharp band of solute, which is allowed to dissolve in a solvent flowing
laminarly in an empty tube, can be described in the limit of a long column as a Gaussian distribution,
the variance of which, σ 2 , in length units is:
where:
()
2
σx = 2D
t
eff
t time of migration of the peak
Deff effective diffusion coefficient given by,
r u
Deff = D12
+
48D
2 2
12
where:
u average solvent velocity
r inner radius of the tube
D12 binary diffusion coefficient.
The first term describes the longitudinal diffusion in the axial direction. The second
term is called the Taylor diffusion coefficient and describes band broadening due to the parabolic
flow profile and therefore radial diffusion. The height equivalent to a theoretical
plate, H, is a measure of the relative peak broadening and is defined as
()
2
H =σ x / L
where:
L length of the tubing.
Combining the above equations yields
2 2D12
r u
H = +
u 24D
12
Bulk diffusivity can be calculated from the above equation.