Supercritical fluids diffusion rate

We know that solubility of the solute(s) can be directly correlated to solvent density, as can diffusivity of the solute into and through the solvent.Typically, solubility increases with density, while diffusivity decreases. Density is strictly a function of temperature and pressure. Similarly, mass transfer increases with reduced solvent viscosity and increasing agitation t l generally, viscosity increases with temperature for a supercritical fluid.The rate of solvation is dependent on the concentrations of both the solvent and solute and the density and temperature of the solvent. Concentration is fixed by flow rate, solvent volume, and contaminant loading. Thus,... 

The slight variation in r(371°) can be explained as follows. The rate constants for 1°, 2°, or 3° hydrogen abstractions by Cl from alkanes are nearly diffusion-controlled in conventional solvents. Consequently, the intrinsic selectivity of Cl is diminished in conventional solvents because of the onset of diffusion control. In the gas phase, selectivity is slightly higher because the barrier imposed by diffusion is eliminated. The viscosity of a supercritical fluid (a) lies between that of conventional fluid solvent and the gas phase and (b) varies with pressure. Because of the low viscosity of supercritical fluids, bimolecular rate constants greater than the 10 ° M" s diffusion-controlled limit can be realized in SCF and, as a consequence, enhanced selectivity is achieved. Consistent with this interpretation is the observation that the plot of r(371°) versus inverse viscosity is approximately linear (Figure 4.4-7) [51]. 

Reaction schemes exploiting supercritical fluid diffusivities. The dif-fusivity of a dilute solute in a supercritical fluid, somewhat removed from the critical point, is typically an order of magnitude greater than in liquid solvents at comparable temperatures. Thus, radical initiators under supercritical fluid conditions are able to escape more readily from solvent cages, and the rate coefficient for the initiation process is markedly increased. Processes propagated by free radicals, such as polymerisation, are rate enhanced for this reason, as are enzymatic reactions. 

However, many enzymes show higher activity in mixtures of organic solvents with water than in pure water [23] and further, the native cellular microenvironment of enzymes is typically composed of lipids, proteins and other substances in addition to water. Since, in aqueous systems, the rate-determining step is often substrate diffusion in the vicinity of the active site of the enzyme [24, 25], supercritical fluid solvents have been perceived as an advantageous alternative. Kinetic studies showed that diffusion is still rate limiting, but that supercritical-fluid diffusivities were beneficial to the reaction rate [26-29]. 

Principles and Characteristics Supercritical fluid extraction uses the principles of traditional LSE. Recently SFE has become a much studied means of analytical sample preparation, particularly for the removal of analytes of interest from solid matrices prior to chromatography. SFE has also been evaluated for its potential for extraction of in-polymer additives. In SFE three interrelated factors, solubility, diffusion and matrix, influence recovery. For successful extraction, the solute must be sufficiently soluble in the SCF. The timescale for diffusion/transport depends on the shape and dimensions of the matrix particles. Mass transfer from the polymer surface to the SCF extractant is very fast because of the high diffusivity in SCFs and the layer of stagnant SCF around the solid particles is very thin. Therefore, the rate-limiting step in SFE is either... 

As its name suggests, supercritical fluid extraction (SEE) relies on the solubilizing properties of supercritical fluids. The lower viscosities and higher diffusion rates of supercritical fluids, when compared with those of liquids, make them ideal for the extraction of diffusion-controlled matrices, such as plant tissues. Advantages of the method are lower solvent consumption, controllable selectivity, and less thermal or chemical degradation than methods such as Soxhlet extraction. Numerous applications in the extraction of natural products have been reported, with supercritical carbon dioxide being the most widely used extraction solvent. However, to allow for the extraction of polar compounds such as flavonoids, polar solvents (like methanol) have to be added as modifiers. There is consequently a substantial reduction in selectivity. This explains why there are relatively few applications to polyphenols in the literature. Even with pressures of up to 689 bar and 20% modifier (usually methanol) in the extraction fluid, yields of polyphenolic compounds remain low, as shown for marigold Calendula officinalis, Asteraceae) and chamomile Matricaria recutita, Asteraceae). " ... 

Small changes in the temperature or pressure of a supercritical fluid may result in great changes in its viscosity and in the diffusivity and solubility of compounds dissolved within it. In such systems, the bioconversion rate is increased thanks to the high diffusion rates which facilitate transport phenomena. In some cases a high diffusion rate can also facilitate product separation. 

Enhanced Mass Transfer, Diffusivity Supercritical fluids share many of the advantages of gases, including lower viscosities and higher diffusivities relative to liquid solvents, thereby potentially providing the opportunity for faster rates, particularly for diffusion-limited reactions. 

Propane or propane/C02 mixtures as liquid, near-critical, or supercritical fluids enhance the solubility of fats and oils (Harrod et al., 2000 Weidner and Richter, 1999). The decrease in viscosity and increase in diffusivity results in a higher hydrogenation rate (Figure 14.4). Harrod et al. (2000) have also demonstrated activity increases by reducing mass-transfer limitations in supercritical propane. 

Organic chemists have been attracted for a variety of reasons to supercritical media as an environment for performing reactions. These reasons include, especially for C02 and H20, the environmental friendliness of the medium. The fact that supercritical fluids can be removed without a residue is an advantage. Other advantages include the solubility of gases within supercritical mixtures, the high diffusion rates, and the variable and adjustable density, solvent power, and dielectric constant of the medium. Ordinary gases, such as 02 and H2, are miscible with... 

Enzymatic reactions in non-aqueous solvents are subjected to a wide interest. A particular class of these solvents is the supercritical fluid (1) such as carbon dioxide that has many advantages over classical organic solvents or water no toxicity, no flammability, critical pressure 7.38 Mpa and temperature 31°C, and allowing high mass transfer and diffusion rates. 

The prospect of using enzymes as heterogeneous catalysts in scC02 media has created significant interest. Their low viscosity and high diffusion rates offer the possibility of increasing the rate of mass-transfer controlled reactions. Also, because enzymes are not soluble in supercritical fluids, dispersion of the free enzymes potentially allows simple separations without the need for immobilization. 

When carbon dioxide is heated beyond its critical point, with a critical temperature of tc = 31.0 °C, a critical pressure of pc = 7.38 MPa, and a critical density of Pc = 0.47 g cm , the gaseous and the liquid phase merge into a single supercritical phase (SC-CO2) with particular new physical properties very low surface tension, low viscosity, high diffusion rates, pressure-dependent adjustable density and solvation capability ( solvation power ), and miscibility with many reaction gases (H2, O2, etc.). It can dissolve solids and liquids. The relative permittivity of an sc-fluid varies linearly with density, e.g. for SC-CO2 at 40 °C, r = 1.4 1.6 on going from 108 to 300 bar. This... 

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