Near-critical

Pitzer K S 1995 Ionic fluids near-critical and related properties J. Phys. Chem. 99 13 070... 

Near critical points, special care must be taken, because the inequality L will almost certainly not be satisfied also, cridcal slowing down will be observed. In these circumstances a quantitative investigation of finite size effects and correlation times, with some consideration of the appropriate scaling laws, must be undertaken. Examples of this will be seen later one of the most encouraging developments of recent years has been the establishment of reliable and systematic methods of studying critical phenomena by simulation. 

Criticality Precautions. The presence of a critical mass of Pu ia a container can result ia a fission chain reaction. Lethal amounts of gamma and neutron radiation are emitted, and a large amount of heat is produced. The assembly can simmer near critical or can make repeated critical excursions. The generation of heat results eventually ia an explosion which destroys the assembly. The quantity of Pu required for a critical mass depends on several factors the form and concentration of the Pu, the geometry of the system, the presence of moderators (water, hydrogen-rich compounds such as polyethylene, cadmium, etc), the proximity of neutron reflectors, the presence of nuclear poisons, and the potential iateraction with neighboring fissile systems (188). As Httle as 509 g of Pu(N02)4 solution at a concentration Pu of 33 g/L ia a spherical container, reflected by an infinite amount of water, is a critical mass (189,190). Evaluation of criticaUty controls is available (32,190). 

Erequenfly, the term compressed fluid, a more general expression than supercritical fluid, is used. A compressed fluid can be either a supercritical fluid, a near-critical fluid, an expanded Hquid, or a highly compressed gas, depending on temperature, pressure, and composition. 

Polymers and Supercritical Fluids. Prior to the mid-1980s, Httie information was pubhshed regarding polymer processing with supercritical and near-critical fluids (1). In 1985, the solubiUties of many polymers in near- and supercritical CO2 were reported. These polymers were examined for thek abiUty to increase viscosity in C02-enhanced oil recovery (24). Since then, a number of studies have examined solubiUties of polymers in... 

Catchpole-Kinp examined binaiy diffusion data of near-critical fluids in the reduced density range of 1 to 2.5 and found that their data correlated with average deviations of 10 percent and a maximum deviation of 60 percent. They observed two classes of behavior. For the first, no correction fac tor was required R = 1). That class was comprised of alcohols as solvents with aromatic or ahphatic solutes, or carbon dioxide as a solvent with ahphatics except ketones as solutes, or... 

This equation is cubic in hquid depth. Below a minimum value of Ejp there are no real positive roots above the minimum value there are two positive real roots. At this minimum value of Ejp the flow is critical that is, Fr = 1, V= V, and Ejp = (3/2)h. Near critical flow conditions, wave motion ana sudden depth changes called hydraulic jumps are hkely. Chow (Open Channel Hydraulics, McGraw-Hill, New York, 1959), discusses the numerous surface profile shapes which may exist in nommiform open channel flows. 

Extraction from Aqueous Solutions Critical Fluid Technologies, Inc. has developed a continuous countercurrent extraction process based on a 0.5-oy 10-m column to extract residual organic solvents such as trichloroethylene, methylene chloride, benzene, and chloroform from industrial wastewater streams. Typical solvents include supercritical CO9 and near-critical propane. The economics of these processes are largely driven by the hydrophihcity of the product, which has a large influence on the distribution coefficient. For example, at 16°C, the partition coefficient between liquid CO9 and water is 0.4 for methanol, 1.8 for /i-butanol, and 31 for /i-heptanol. 

Margules, and Scatchard-Hildebrand) are particular mathematical solutions to Eq. (48) these models do not satisfy Eqs. (45) and (46), except in the limiting case where the right-hand sides of these equations vanish. This limiting case provides a good approximation for mixtures at low pressures but introduces serious error for mixtures at high pressures, especially near critical conditions. 

Chao and Seader assume that the partial molar volumes are independent of composition this assumption is equivalent to saying that at constant temperature and pressure there is no volume change upon mixing the pure liquid components, be they real or hypothetical. The term on the right-hand side of Eq. (46) is assumed to be zero for all temperatures, pressures, and compositions. This assumption is very poor near critical conditions, and is undoubtedly the main reason for the poor performance of the Chao-Seader correlation in the critical region. 

Clouter M. J., Kiefte H, Ali N. Anomalous behaviour in the vibrational Raman spectrum of oxygen under near-critical conditions, Phys. Rev. 

Sovova, H., Near-critical extraction of pigments and oleoresin from stinging nettle leaves, J. Supercrit. Fluids, 30, 213, 2004. 

The tuning of solubility with a relatively small jump or fall in pressure can possibly bestow many benefits with respect to rates, yields, and selectivity. Reaction parameters can be changed over a wide range. Replacement of solvents with high boiling points by supercritical (SC) fluids offers distinct advantages with respect to removal of the solvent. SC fluids like CO2 are cheap and environmentally friendly the critical temperature of CO2 is 31 C and the critical pressure 73.8 atm (Poliakoff and Howdle, 1995). Eckert and Chandler (1998) have given many examples of the use of SC fluids. Alkylation of phenol with tcrt-butanol in near critical water at 275 °C allows 2- erf-butyl phenol to be formed (a major product when the reaction is kinetically controlled 4-rert-butyl phenol is the major product, when the reaction is... 

Koch and Leitner (1998) have recently conducted the oxoreaction of 1-octene with CO and H2, using a Rh-based catalyst, in SC CO2. Fischer era/. (1999) have reported enhancements in selectivity by a factor of 4 to 18 with near critical ammonia, during Co- and Ni-catalysed synthesis of 1,3-diaminopropane. This is attributed to a higher concentration of ammonia at the catalyst surface. 

Adrian et al. (2000) have reported a novel high-pressure liquid-liquid extraction process with reference to processing in biotechnology the example of cardiac glycosides (digitoxin and digoxin) is cited. A completely miscible, binary system of water and a hydrophobic organic solvent like ethanol can split into two liquid phases when a near-critical gas (e.g. CO2) is added. The near-critical C02/water/l-propanol system is reported, for which possibilities for industrial exploitation exist. 

Mukhopadhyay, Natural Extracts Using Supercritical Carbon Dioxide, CRC Press, Boca Raton, Fla., 2000 Moyler, Extraction of flavours and fragrances with compressed CO2, in Extraction of Natural Products Using Near-Critical Solvents, King and Bott (eds.), Blackie Academic Professional, London, 1993. 

Near-critical water has been used as a medium for various C-C bond formation reactions including Friedel-Crafts alkylation and acylation (Eq. 7.12).30 In these reactions, near-critical water solubilizes the organics and acts as a source of both hydronium and hydroxide ions, thereby replacing the normally required hazardous solvents and catalysts that require subsequent neutralization and disposal. 

Bishop, A. A., R. O. Sandberg, and L. S. Tong, 1965, Forced Convection Heat Transfer to Water at Near-Critical Temperature and Super-Critical Pressures, USAEC Rep. WCAP-2056-Part IIIB, and also Paper 2-7, AlChE/IChE Joint Meeting, London, June, 1965. (4)... 

For the relaxation of the solid near the gel point, the critical gel may serve as a reference state. The long time asymptote of G(t) of the nearly critical gel, the equilibrium modulus Ge, intersects the G(t) = St n of the critical gel at a characteristic time (Fig. 6) which we will define as the longest relaxation time of the nearly critical gel [18]... 

Only two of the exponents (a and n, for instance) are sufficient to describe the rheology of nearly critical gels. The front factor is more difficult to estimate, but it most likely differs on both sides. 

The simplest expression incorporating the basic features of self-similarity and cut-off for nearly critical gels has the spectrum of the critical gel altered by a cut-off at the longest time [19] ... 

Adolf and Martin [15] postulated, since the near critical gels are self-similar, that a change in the extent of cure results in a mere change in scale, but the functional form of the relaxation modulus remains the same. They accounted for this change in scale by redefinition of time and by a suitable redefinition of the equilibrium modulus. The data were rescaled as G /Ge(p) and G"/Ge(p) over (oimax(p). The result is a set of master curves, one for the sol (Fig. 23a) and one for the gel (Fig. 23 b). 

A second observation relates to calculations near critical points. The coexistence lines in Fig. 10.7 do not extend above a temperature of T = 11.6 because above that temperature significant overlap exists between the liquid and vapor peaks of the histograms. This overlap renders calculations of the liquid and gas densities imprecise. 

Larger system sizes suffer less from this effect and can be used to obtain coexistence densities near critical points. 

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