The experimental evidence for the behaviour of the binary diffusion coefficient for a solute in dilute solution in a supercritical fluid (a fluid above its critical temperature and pressure) is reviewed. Measurements at very low dilution, particularly by the Taylor dispersion technique, indicate that, at constant temperature a few degrees above the critical temperature, the product of density and the diffusion coefficient exhibits a small, continuous and undramatic variation from zero density to well above the critical density. However, some measurements made at higher, but still very low concentrations (e.g. with mole fractions around 10
-3
), show a lowering of the coefficient in the critical region. The equations, based on non-equilibrium thermodynamics, are put into a form in which the behaviour of the binary diffusion coefficient in the critical region, but not very close to the critical point, may be examined using an equation of state. Calculations for naphthalene in solution in carbon dioxide are carried out using the van der Waals equation of state for mixtures to indicate the form and order of magnitude of the ‘anomalous’ lowering of the coefficient, and especially its dependence on concentration. These indicate a substantial effect even at naphthalene mole fractions of 4.0 x 10
-4
or less and a temperatures 1, 3 and 9 K above the critical temperature of the pure solvent. In addition the flux of a solute in a supercritical fluid in the critical region with respect to space or cell-fixed coordinates is discussed. Because of the large and negative partial molar volumes of solutes like naphthalene in this region, the frames of reference, according to which the diffusion coefficients are defined, can be caused to move rapidly, commonly towards the source of concentration. Thus fluxes of solute with respect to space-fixed coordinates are further substantially reduced in the critical region. The combination of the lowering of the diffusion coefficient and barycentric motion can therefore cause a very significant reduction of solute mass transfer in the critical region and may be the explanation of the sometimes very large diffusion anomalies observed experimentally.
Microfluidic osmotic compression of a charge-stabilized colloidal dispersion: Equation of state and collective diffusion coefficient
