Density deviation

Molecules are in continuous random motion, and as a result of this, small volume elements within the liquid continuously experience compression or rarefaction such that the local density deviates from the macroscopic average value. If we represent by 6p the difference in density between one such domain and the average, then it is apparent that, averaged over all such fluctuations, 6p = 0 Equal contributions of positive and negative 6 s occur. However, if we consider the average value of 6p, this quantity has a nonzero value. Of these domains of density fluctuation, the following statements can be made ... 

Relevant for the following discussion is the equation of state in the form e(p), at T 0. Although both the pressure and the energy density deviate sizably from their ideal values, cf. Figure 6, we observe an almost linear relation... 

Here pg and p f are the mass densities of the gel and the solvent, respectively, K is a bulk modulus, c0 is the speed of sound, and i s is the solvent shear viscosity. The solvent bulk viscosity has been neglected. The terms proportional to / arise from an elastic coupling in the free energy between the density deviation of gel and that of solvent The p in Eq. (6.1) coincides with the shear modulus of gels treated so far. We neglect the frequency-dependence of the elastic moduli. It can be important in dynamic light scattering, however, as will be discussed in the next section. 

The results of the pycnometric determinations are presented in terms of apparent densities of the clays in the various displacement fluids. The apparent density of a clay is that density calculated from the data by the assumption that the density of the displacement fluid is normal throughout the liquid phase. When dissimilarities are observed for the apparent densities using different displacement fluids and the apparent densities deviate from the actual density, the possibility of density abnormalities of the liquid in the proximity of the clay surface should be considered. Moreover, consideration must also be given to another possible cause of certain deviations—i.e., the existence of a void space within the clay system which is inaccessible to the liquid. 

Uniformity of the current density over the whole area of the electrode is important for the interpretation of current-potential data. We recall that the measured quantities are the total current and the potential at a certain point in solution, where the reference electrode (or the tip of the Luggin capillary) is located. From this we can calculate the average current density, but not its local value. As for the potential, we have already noted that unless the cell is properly designed, the potential measured may be grossly in error if the reference electrode is located at a point where the local current density deviates significantly from its average value, as shown in Fig. 6C. 

The relationship between the Fermi correlation and the spatial localization of electrons is developed by defining, as McWeeny (1960) does, a correlation function/(rj, rj) in an expression which determines the extent to which the pair density deviates from a simple product of number densities,... 

Real gases follow the ideal gas equation of state only at sufficiently low densities. Deviations appear in a variety of forms. Boyle s law, PV = C, is no longer satisfied at high pressures, and Charles s law, V T, begins to break down at low temperatures. Deviations from the predictions of Avogadro s hypothesis appear for... 

The dependence of viscosity upon pressure is principally a density effect. Estimation of vapor viscosity at elevated pressures is commonly done by correlating density deviations from the low-pressure values, which are in turn estimated by using the procedures mentioned above. Several methods are available, but the method developed by Jossi et al. and extended to polar fluids by Stiel and Thodos is relatively accurate and easy to apply. 

The density anomaly of the Baltic Sea is chiefly caused by a significant excess of calcium bicarbonate discharged from the rivers. The resulting density deviation of brackish water in the Baltic Sea can be estimated by the empirical relation between absolute salinity 5a, determined from density measurements, and practical salinity 5, determined from conductivity (Millero and Kremhng, 1976),... 

SCWO reactor conditions of 250 bar and 6(X) t. the density deviation of SCW from an ideal gas is fairly small. The compressibility factor Z (= 1 for an ideal gas) at these conditions is 0.88. 

Other observations of this test work, with respect to key alkylate product properties, were that neither the Reid vapor pressure (RVP) nor density deviated significantly from values that would be obtained via liquid acid alkylation. Further, acid-soluble oils (ASO), formed as contaminant side products in the case of liquid acid processes, could not be detected among the reaction products in our SAC testing. Compared with the liquid acid technologies, this effect results in both lower feed consumption per unit of alkylate production and eliminates generation of a by-product that can be difficult to dispose of. 

Figure 4 shows that, at low deposition density, the density of surface V=0 species linearly increased with that of deposited vanadium in parallel with a theoretical line representing an ideal monolayer of V2O5 calculated on the assumption of one V=0 in one unit cell of V2O5 crystal (15.78 pmol m [9]). An intercept in x-axis corresponds to the isolated or monomeric V=0 species that are inactive in NO-NH3 reaction [15]. The V=0 density deviated from the... 

The behavior of B(p) and C(p) for propane is shown in Figure 7. The number of PpT data used here for adjusting the equation of state is 843, with different least-squares weightings than in Refs. 3 and 5. Overall deviations, with equal weighting for all points, are 2.07 bar for the mean of absolute pressure deviations and 0.34% for the rms of relative density deviations. 

With compound films, changes in stoichiometry by dissociation, fractionating and incomplete recombination or formation of other chemical compounds may contribute to density deviations. 

The density of archaeological wood will at best be equal to the values for recent wood at worst, it will approach zero as the wood nears total destruction. In general, density will be somewhere between these limits. The degree to which the density deviates from values of recent wood is a measure of the extent of deterioration. However, it is not unusual to find archaeological wood that has significantly lower strength properties than recent wood without showing any reduction in density 4, 5). 

Hence, the steady state flux through an iron membrane under pure diffusion control should be proportional to the square root of the cathodic current density. Deviations from the square root dependence have been observed [116, 117], particularly at extreme current densities, but this relationship seems to hold generally [7, 118). The relationship between Joo and rj can also be derived, and values of dr]/d nJcx for coupled discharge-recombination and other mechanisms are shown in Table 8 [6],... 

The stopping criterion depends on the specific properties to be fitted. For example, if the density deviates by less than 0.5 % from experiment, the corresponding force field is considered as optimal because the experiment is not more accurate either. The same holds for all other properties. However, the experimental accuracy is much lower for transport properties like diffusion coefficients or viscosity. 

Unlike the dependencies of density deviation (from additive values) on system composition, correspondent dependencies of specific (molar) volume deviation from the additive values ... 

Interaction is accompanied by formation of the heteromolecular associates. It can be demonstrated by analysis of volumetric equations for the liquid mixed systems, data on volume compression, i.e., positive density deviation from additivity rule, and hence negative deviations of experimental specific molar volume from partial molar volume additivity rule. 

Figure 3.9 Density deviation plot for R125 (pentafluo-roethane) for the PPDS and Rackett equation. (Data from Widiatmo et al. [46].)...

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