Supercritical fluids diffusion coefficients

A number of other methods, not falling within any of the earlier-mentioned categories, may prove useful for process intensification. Some of them, such as supercritical fluids, are already known and have been applied in other industries (104,105). Because of their unique properties, especially the high diffusion coefficient, supercritical fluids are attractive media for mass transfer operations,... 

The development of mass transfer models require knowledge of three properties the diffusion coefficient of the solute, the viscosity of the SCF, and the density of the SCF phase. These properties can be used to correlate mass transfer coefficients. At 35 C and pressures lower than the critical pressure (72.83 atm for CO2) we use the diffusivity interpolated from literature diffusivity data (2,3). However, a linear relationship between log Dv and p at constant temperature has been presented by several researchers U>5) who correlated diffusivities in supercritical fluids. For pressures higher than the critical, we determined an analytical relationship using the diffusivity data obtained for the C02 naphthalene system by lomtev and Tsekhanskaya (6), at 35 C. 

Klask, U. (1998) Diffusion coefficients in fluids — Determination of binary diffusion coefficients of organic substances in supercritical cEirbon dioxide with the Taylor dispersion method (in German), Doctoral dissertation. University of Bochum, Germany published 1999 by Shaker, Aachen. 

Transport Properties Although the densities of supercritical fluids approach those of conventional hquids, their transport properties are closer to those of gases, as shown for a typical SCF such as CO9 in Table 22-12. For example, the viscosity is several orders of magnitude lower than at liquidlike conditions. The self-diffusion coefficient ranges between 10" and 10" em /s, and binaiy-diffusiou coefficients are similar [Liong, Wells, and Foster, J. Supercritical Fluids 4, 91 (1991) Catchpole and King, Ind. Eng. Chem. Research, 33,... 

Supercritical fluid chromatography (SFC) refers to the use of mobile phases at temperatures and pressures above the critical point (supercritical) or just below (sub-critical). SFC shows several features that can be advantageous for its application to large-scale separations [132-135]. One of the most interesting properties of this technique is the low viscosity of the solvents used that, combined with high diffusion coefficients for solutes, leads to a higher efficiency and a shorter analysis time than in HPLC. 

A supercritical fluid exhibits physical-chemical properties intermediate between those of liquids and gases. Mass transfer is rapid with supercritical fluids. Their dynamic viscosities are nearer to those in normal gaseous states. In the vicinity of the critical point the diffusion coefficient is more than 10 times that of a liquid. Carbon dioxide can be compressed readily to form a liquid. Under typical borehole conditions, carbon dioxide is a supercritical fluid. 

Supercritical fluid extraction (SFE) is a technique in which a supercritical fluid [formed when the critical temperature Tf) and critical pressure Pf) for the fluid are exceeded simultaneously] is used as an extraction solvent instead of an organic solvent. By far the most common choice of a supercritical fluid is carbon dioxide (CO2) because CO2 has a low critical temperature (re = 31.1 °C), is inexpensive, and is safe." SFE has the advantage of lower viscosity and improved diffusion coefficients relative to traditional organic solvents. Also, if supercritical CO2 is used as the extraction solvent, the solvent (CO2) can easily be removed by bringing the extract to atmospheric pressure. Supercritical CO2 itself is a very nonpolar solvent that may not have broad applicability as an extraction solvent. To overcome this problem, modifiers such as methanol can be used to increase the polarity of the SFE extraction solvent. Another problem associated with SFE using CO2 is the co-extraction of lipids and other nonpolar interferents. To overcome this problem, a combination of SFE with SPE can be used. Stolker et al." provided a review of several SFE/SPE methods described in the literature. 

Table 3.12 Density, viscosity, and diffusion coefficient of gas, liquid and supercritical fluids...

The first use of supercritical fluid extraction (SFE) as an extraction technique was reported by Zosel [379]. Since then there have been many reports on the use of SFE to extract PCBs, phenols, PAHs, and other organic compounds from particulate matter, soils and sediments [362, 363, 380-389]. The attraction of SFE as an extraction technique is directly related to the unique properties of the supercritical fluid [390]. Supercritical fluids, which have been used, have low viscosities, high diffusion coefficients, and low flammabilities, which are all clearly superior to the organic solvents normally used. Carbon dioxide (C02, [362,363]) is the most common supercritical fluid used for SFE, since it is inexpensive and has a low critical temperature (31.3 °C) and pressure (72.2 bar). Other less commonly used fluids include nitrous oxide (N20), ammonia, fluoro-form, methane, pentane, methanol, ethanol, sulfur hexafluoride (SF6), and dichlorofluoromethane [362, 363, 391]. Most of these fluids are clearly less attractive as solvents in terms of toxicity or as environmentally benign chemicals. Commercial SFE systems are available, but some workers have also made inexpensive modular systems [390]. 

Supercritical fluids possess favorable physical properties that result in good behavior for mass transfer of solutes in a column. Some important physical properties of liquids, gases, and supercritical fluids are compared in Table 4.1 [49]. It can be seen that solute diffusion coefficients are greater in a supercritical fluid than in a liquid phase. When compared to HPLC, higher analyte diffusivity leads to lower mass transfer resistance, which results in sharper peaks. Higher diffusivity also results in higher optimum linear velocities, since the optimum linear velocity for a packed column is proportional to the diffusion coefficient of the mobile phase for liquid-like fluids [50, 51]. 

The diffusion coefficients of small molecular weight solutes in supercritical fluids and liquids are typically in the range of 1 x 10 " and 10 cm /s [18,19], respectively, while those of EFLs are typically intermediate [4] between these two values (10 cm /s). 

Supercritical fluid chromatography provides increased speed and resolution, relative to liquid chromatography, because of increased diffusion coefficients of solutes in supercritical fluids. (However, speed and resolution are slower than those of gas chromatography.) Unlike gases, supercritical fluids can dissolve nonvolatile solutes. When the pressure on the supercritical solution is released, the solvent turns to gas. leaving the solute in the gas phase for easy detection. Carbon dioxide is the supercritical fluid of choice for chromatography because it is compatible with flame ionization and ultraviolet detectors, it has a low critical temperature. and it is nontoxic. 

The shrinking-core model (SCM) is used in some cases to describe the kinetics of solid and semi-solids-extraction with a supercritical fluid [22,49,53] despite the facts that the seed geometry may be quite irregular, and that internal walls may strongly affect the diffusion. As will be seen with the SCM, the extraction depends on a few parameters. For plug-flow, the transport parameters are the solid-to-fluid mass-transfer coefficient and the intra-particle diffusivity. A third parameter appears when disperse-plug-flow is considered [39,53],... 

The supercritical fluid extraction of analytes from solid sorbents is controlled by a variety of factors including the affinity of the analytes for the sorbent, the tortuosity of the sorbent bed, the vapor pressure of the analytes, and the solubility and the diffusion coefficient of the analytes in the supercritical fluid. Additionally, SFE efficiencies are affected by a complex relationship between many experimental variables, several of which are listed in Table I. Although it is well established that, to a first approximation, the solvent power of a supercritical fluid is related to its density, little is known about the relative effects of many of the other controllable variables for analytical-scale SFE. A better understanding of the relative effects of controllable SFE variables will more readily allow SFE extractions to be optimized for maximum selectivity as well as maximum overall recoveries. 

Supercritical fluid extraction (SFE) procedures have been developed for extractions of species of elements from samples. Viscosities and diffusion coefficients... 

Table 3.3 presents the approximate physical properties of gases, supercritical fluids, and liquids. It shows that the densities of supercritical fluids are close to that of a liquid, whereas their viscosities are gaslike. The diffusion coefficients are in between. Due to these unique properties, supercritical fluids have good solvating power (like liquid), high diffusivity (better than liquid), low viscosity, and minimal surface tension (like gas). With rapid mass transfer in the supercritical phase and with better ability to penetrate the pores in a matrix, extraction is fast in SFE, along with high extraction efficiency. 

Accelerated solvent extraction (ASE) is also known as pressurized fluid extraction (PFE) or pressurized liquid extraction (PLE). It uses conventional solvents at elevated temperatures (100 to 180°C) and pressures (1500 to 2000 psi) to enhance the extraction of organic analytes from solids. ASE was introduced by Dionex Corp. (Sunnyvale, CA) in 1995. It evolved as a consequence of many years of research on SFE [45], SFE is matrix dependent and often requires the addition of organic modifiers. ASE was developed to overcome these limitations. It was expected that conventional solvents would be less efficient than supercritical fluids, which have higher diffusion coefficients and lower viscosity. However, the results turned out to be quite the opposite. In many cases, extraction was faster and more complete with organic solvents at elevated temperature and pressure than with SFE. Extensive research has been done on the extraction of a variety of samples with ASE. ASE was approved by EPA as a standard method in 1996. 

There are several reasons why SFC may gain its place as a separation technique alongside GC and LC in the years ahead. From a fundamental point of view, the diffusion coefficients under typical SFC conditions are lower than those typically encountered in gases, but higher than those found in liquids. The viscosity of supercritical fluids is usually higher than that of typical gases, but much lower than that of common liquids. At the same time, supercritical fluids are good solvents for many low-volatile solutes, which are not compatible with GC. Therefore, SFC may offer the possibility to separate non-volatile... 

The aim of this Chapter is the development of an uniform model for predicting diffusion coefficients in gases and condensed phases, including plastic materials. The starting point is a macroscopic system of identical particles (molecules or atoms) in the critical state. At and above the critical temperature, Tc, the system has a single phase which is, by definition, a gas or supercritical fluid. The critical temperature is a measure of the intensity of interactions between the particles of the system and consequently is a function of the mass and structure of a particle. The derivation of equations for self-diffusion coefficients begins with the gaseous state at pressures p below the critical pressure pc. A reference state of a hypothetical gas will be defined, for which the unit value D = 1 m2/s is obtained at p = 1 Pa and a reference temperature, Tr. Only two specific parameters, Tc, and the critical molar volume, VL, of the mono-... 

Cabrera, C. R. and Bard A. J. (1989) Electrochemistry in near-critical and supercritical fluids. Part 8. Methyl viologen, decamethylferrocene, Os (bpy)2+ and ferrocene in acetonitrile and the effect of pressure on diffusion coefficients under supercritical conditions. J. Electroanal. Chem. 273, 147-160. 

---