Dense fluid

The most significant differences of the various profiles shown, Fig. 3.7, occur at the lowest frequencies. Albeit the measurements do not extend down to zero frequency, it seems clear that at the lowest frequencies the intercollisional process has affected the profiles. We notice the beginning of a dip similar to the ones seen in Fig. 3.5. At the higher densities the intercollisional wing of the inverted Lorentzian extends to much higher frequencies, the more so the higher the densities are the intercollisional dip persists to the highest densities. 

Similar results were also obtained for argon-krypton mixtures [252]. Apart from the low-frequency region of the intercollisional dip, the variation of the translational line shape is rather subtle reduced absorption profiles of a number of rare gas mixtures at near-liquid densities (up to 750 amagat) have been proposed which ignore these variations totally [252], 

1 Symmetrized spectral functions are sometimes used when dealing with near classical systems. In this case, the function shown in Fig. 3.8 is the same as Vg(v) of Eq. 3.2, multiplied by tanh (hcv/2kT) Vg(v) and the symmetrized function differ very little at low frequencies. 

The decrease of yo with density, on the other hand, is related to interference. A general explanation must be sought in terms of the symmetries that exist at high densities a neon atom in a cage of argon atoms interacts very little with radiation, on account of the near inversion symmetry, which is inconsistent with a dipole. 

The translational spectra of pure liquid hydrogen have been recorded with para-H2 to ortho-H2 concentration ratios of roughly 25 75, 46 54 and 100 0, Fig. 3.9 [201, 202]. For the cases of non-vanishing ortho-H2 concentrations, the spectra have at least a superficial similarity with the binary translational spectra compare with the data shown for low frequencies ( 250 cm-1) of Fig. 3.10 below. A comparison of the spectral moments of the low-density gas and the liquid shows even quantitative agreement within the experimental uncertainties which are, however, substantial. 

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Two generally accepted models for the vapor phase were discussed in Chapter 3 and one particular model for the liquid phase (UNIQUAC) was discussed in Chapter 4. Unfortunately, these, and all other presently available models, are only approximate when used to calculate equilibrium properties of dense fluid mixtures. Therefore, any such model must contain a number of adjustable parameters, which can only be obtained from experimental measurements. The predictions of the model may be sensitive to the values selected for model parameters, and the data available may contain significant measurement errors. Thus, it is of major importance that serious consideration be given to the proper treatment of experimental measurements for mixtures to obtain the most appropriate values for parameters in models such as UNIQUAC. 

The introductory remarks about unimolecular reactions apply equivalently to bunolecular reactions in condensed phase. An essential additional phenomenon is the effect the solvent has on the rate of approach of reactants and the lifetime of the collision complex. In a dense fluid the rate of approach evidently is detennined by the mutual difhision coefficient of reactants under the given physical conditions. Once reactants have met, they are temporarily trapped in a solvent cage until they either difhisively separate again or react. It is conmron to refer to the pair of reactants trapped in the solvent cage as an encounter complex. If the unimolecular reaction of this encounter complex is much faster than diffiisive separation i.e., if the effective reaction barrier is sufficiently small or negligible, tlie rate of the overall bimolecular reaction is difhision controlled. 

Dardi P S and Dahler J S 1990 Microscopic models for iodine photodissociation quantum yields in dense fluids J. Chem. Phys. 93 242-56... 

The excess chemiccil potential is thus determined from the average of exp[—lT (r )/fe In ensembles other than the canonical ensemble the expressions for the excess chem potential are slightly different. The ghost particle does not remain in the system and the system is unaffected by the procedure. To achieve statistically significant results m Widom insertion moves may be required. However, practical difficulties are encounte when applying the Widom insertion method to dense fluids and/or to systems contain molecules, because the proportion of insertions that give rise to low values of y f, dramatically. This is because it is difficult to find a hole of the appropriate size and sha... 

Pressure Drop. The pressure drop across a two-phase suspension is composed of various terms, such as static head, acceleration, and friction losses for both gas and soflds. For most dense fluid-bed appHcations, outside of entrance or exit regimes where the acceleration pressure drop is appreciable, the pressure drop simply results from the static head of soflds. Therefore, the weight of soflds ia the bed divided by the height of soflds gives the apparent density of the fluidized bed, ie... 

When shearing high-velocity flow of dense fluids, the gate assemblies shake violently, and for this seiwice solid-wedge or flexible-... 

P. Attard, D. R. Berard, C. P. Ursenbach, G. N. Patey. Interaction free energy between planar walls in dense fluids an Omstein-Zernike approach for hard-sphere, Lennard-Jones, and dipolar systems. Phys Rev A 44 8224-8234, 1991. 

I. K. Snook, W. van Megen. Solvation forces in simple dense fluids. J Chem Phys 72 2907-2913, 1980. 

The behavior of assoeiating fluid near the hard wall was extensively studied in the framework of the theory diseussed above. The model of Cummings and Stell was applied to relatively dense fluids at a high degree of dimerization [33,36]. Fig. 1 presents the density profiles ealeulated within the framework of the eombined PYl/EMSA theory (i.e., the density profiles were evaluated from the PY 1 equation, whereas the bulk direet eorrelation fune-tions follow from the EMSA equation) and HNCl/EMSA approximations [33]. The ealeulations were performed for L = 0.42[Pg.181]

In dense fluids an additional complication appears, connected with the hydrodynamic nature of the slow collective motion that the molecule performs together with its neighbourhood. According to [59] it results in rather general asymptotic decay Kj(t) oc t 5/2 at times much larger than... 

This is an indication of the collective nature of the effect. Although collisions between hard spheres are instantaneous the model itself is not binary. Very careful analysis of the free-path distribution has been undertaken in an excellent old work [74], It showed quite definite although small deviations from Poissonian statistics not only in solids, but also in a liquid hard-sphere system. The mean free-path X is used as a scaling length to make a dimensionless free-path distribution, Xp, as a function of a free-path length r/X. In the zero-density limit this is an ideal exponential function (Ap)o- In a one-dimensional system this is an exact result, i.e., Xp/(Xp)0 = 1 at any density. In two dimensions the dense-fluid scaled free-path distributions agree quite well with each other, but not so well with the zero-density scaled distribution, which is represented by a horizontal line (Fig. 1.21(a)). The maximum deviation is about... 

One possibility for this was demonstrated in Chapter 3. If impact theory is still valid in a moderately dense fluid where non-model stochastic perturbation theory has been already found applicable, then evidently the continuation of the theory to liquid densities is justified. This simplest opportunity of unified description of nitrogen isotropic Q-branch from rarefied gas to liquid is validated due to the small enough frequency scale of rotation-vibration interaction. The frequency scales corresponding to IR and anisotropic Raman spectra are much larger. So the common applicability region for perturbation and impact theories hardly exists. The analysis of numerous experimental data proves that in simple (non-associated) systems there are three different scenarios of linear rotator spectral transformation. The IR spectrum in rarefied gas is a P-R doublet with either resolved or unresolved rotational structure. In the process of condensation the following may happen. 

The dense fluid that exists above the critical temperature and pressure of a substance is called a supercritical fluid. It may be so dense that, although it is formally a gas, it is as dense as a liquid phase and can act as a solvent for liquids and solids. Supercritical carbon dioxide, for instance, can dissolve organic compounds. It is used to remove caffeine from coffee beans, to separate drugs from biological fluids for later analysis, and to extract perfumes from flowers and phytochemicals from herbs. The use of supercritical carbon dioxide avoids contamination with potentially harmful solvents and allows rapid extraction on account of the high mobility of the molecules through the fluid. Supercritical hydrocarbons are used to dissolve coal and separate it from ash, and they have been proposed for extracting oil from oil-rich tar sands. 

It is often of industrial interest to be able to predict the equilibrium sorption of a gas in a molten polymer (e.g., for devolatilization of polyolefins). Unfortunately, the Prigogine-Flory corresponding-states theory is limited to applications involving relatively dense fluids 3,8). An empirical rule of thumb for the range of applicability is that the solvent should be at a temperature less than 0.85 Tp, where Tp is the absolute temperature reduced by the pure solvent critical temperature. 

H. However, for dense fluids the effects of packing entropy may also be important... 

For a miscible displacement at the required reservoir conditions, carbon dioxide must exist as a dense fluid (in the range 0.5 to 0.8g/cc). Unfortunately, the viscosity of even dense CO2 is in the range of 0.03 to 0.08 cp, no more than one twentieth that of crude oil. When CO2 is used directly to displace the crude, the unfavorable viscosity ratio produces inefficient oil displacement by causing fingering of the CO2, due to frontal instability. In addition, the unfavorable mobility ratio accentuates flow non-... 

Shing, K. S. Gubbins, K. E., The chemical potential in dense fluids and fluid mixtures via computer simulation, Mol. Phys. 1982, 46, 1109-1128... 

The overlap distribution method is more reliable than the direct averaging or single-direction FEP/NEW calculation. For example, it is capable of producing a good estimate of the chemical potential of dense fluids where the latter methods fail... 

Under the simulation conditions, the HMX was found to exist in a highly reactive dense fluid. Important differences exist between the dense fluid (supercritical) phase and the solid phase, which is stable at standard conditions. One difference is that the dense fluid phase cannot accommodate long-lived voids, bubbles, or other static defects, whereas voids, bubbles, and defects are known to be important in initiating the chemistry of solid explosives.107 On the contrary, numerous fluctuations in the local environment occur within a time scale of tens of femtoseconds (fs) in the dense fluid phase. The fast reactivity of the dense fluid phase and the short spatial coherence length make it well suited for molecular dynamics study with a finite system for a limited period of time chemical reactions occurred within 50 fs under the simulation conditions. Stable molecular species such as H20, N2, C02, and CO were formed in less than 1 ps. 

Thus, dendrimers exhibit a unique combination of (a) high molecular weights, typical for classical macromolecular substances, (b) molecular shapes, similar to idealized spherical particles and (c) nanoscopic sizes that are larger than those of low molecular weight compounds but smaller than those of typical macromolecules. As such, they provide unique rheological systems that are between typical chain-type polymers and suspensions of spherical particles. Notably, such systems have not been available for rheological study before, nor are there yet analytical theories of dense fluids of spherical particles that are successful in predicting useful numerical results. 

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