Mixture densities, deviations

Average absolute deviation (percent) of solute solubility (y) and mixture density (p)... 

Soave equation gives rather deviations in mixture density with all mixing rules ... 

Table IV. Summary of Deviations of Predicted Binary Mixture Densities and Methane K-Values from Experimental Data...

Here, Pc is the mixture density of the dense phase. U up i is defined by J Uf-U/), where Uf and U are mean velocities of the dilute and dense phases, respectively. This definition of mesoscale slip velocity differs a little bit from that in the cluster-based EMMS model, because the continuous phase transforms from the dilute phase to the dense phase. And their quantitative difference is l-f)PgUgc/Pc, which is normally negligible for gas-solid systems. Similarly, the closure of Fdi switches to the determination of bubble diameter. And it is well documented in literature ever since the classic work of Davidson and Harrison (1963). Compared to cluster diameter, bubble diameter arouses less disputes and hence is easier to characterize. The visual bubbles are normally irregular and in constantly dynamic transformation, which may deviate much from spherical assumption. Thus, the diameter of bubble here can also be viewed as drag-equivalent definition. 

The O H stretching spectra of ethanol trimers and larger clusters cannot be conformationally resolved in a slit jet expansion [65, 77, 157], VUV-IR spectra [184] are even broader, sometimes by an order of magnitude, and band maxima deviate systematically by up to +50 cm 1 from the direct absorption spectra. We note that ethanol dimers and clusters have also been postulated in dilute aqueous solution and discussed in the context of the density anomaly of water ethanol mixtures [227], Recently, we have succeeded in assigning Raman OH stretching band transitions in ethanol-water, ethanol water, and ethanol water2 near 3550, 3410, and 3430cm, respectively [228],... 

However, two types of systems are sufficienfry important that we can use them almost exclusively (1) liquid aqueous solutions and (2) ideal gas mixtures at atmospheric pressure, hr aqueous solutions we assume that the density is 1 gtcvc , the specific heat is 1 cal/g K, and at any solute concentration, pressure, or temperature there are -55 moles/hter of water, hr gases at one atmosphere and near room temperature we assume that the heat capacity per mole is R, the density is 1/22.4 moles/hter, and aU components obey the ideal gas equation of state. Organic hquid solutions have constant properties within 20%, and nonideal gas solutions seldom have deviations larger than these. 

Tzou TZ. Density, excess molar volume, and vapor pressure of propellant mixtures in metered-dose inhalers deviation from ideal mixtures. Respir Drug Delivery YI, Int Symp 1998 439-443. 

Surface pressure/area isotherms of mixtures of the cationic lipid (20, n = 12) with distearoylphosphatidylcholine (DSPC) are shown in Fig. 30. For all mixtures only one collapse point is observed. The collapse pressure increases continuously with increasing amount of DSPC, indicating miscibility of the two components. Plotting A versus molar ratio (Fie. 3D results in considerable deviation from linearity, which also suggests miscibility of the two compounds in monolayers. This is also confirmed by the fact that the polymerization rate, as measured by the increase of optical density at 540 nm, is reduced by a factor of 100 when the DSPC molar ratio is increased from 0 to 0.52,... 

For ideal mixtures there is a simple relationship between the measurable ultrasonic parameters and the concentration of the component phases. Thus ultrasound can be used to determine their composition once the properties of the component phases are known. Mixtures of triglyceride oils behave approximately as ideal mixtures and their ultrasonic properties can be modeled by the above equations [19]. Emulsions and suspensions where scattering is not appreciable can also be described using this approach [20]. In these systems the adiabatic compressibility of particles suspended in a liquid can be determined by measuring the ultrasonic velocity and the density. This is particularly useful for materials where it is difficult to determine the adiabatic compressibility directly, e.g., powders, biopolymer or granular materials. Deviations from equations 11 - 13 in non-ideal mixtures can be used to provide information about the non-ideality of a system. 

The more obvious and consistent deviations from the hard sphere theory occur, at the low density values, due to the effects of attractive forces in the real system. We can attempt to correct for these effects using a method described previously (27-30) for the analysis of angular momentum correlation times in supercritical CFjj and CFjj mixtures with argon and neon. We replace the hard sphere radial distribution function at contact hs with a function gp (0) which uses the more realistic... 

Dalton s law is not very accurate under conditions at which deviations from ideal behavior are appreciable. The reason for this is that the densities at which partial pressures are calculated may be considerably different from those existing in the gas mixture. Amagat s law is usually more accurate, because the F/s are calculated at the temperature and pressure existing in the mixture. 

The self-diffusion of benzene in PIB [36], cyclohexane in BR [37] and toluene in PIB [38-40] has been investigated by PFG NMR. In addition more recently Schlick and co-workers [41] have measured the self-diffusion of benzene and cyclohexane mixtures in polyisoprene. In the first reported study of this kind, Boss and co-workers [36] measured the self-diffusion coefficients of benzene in polyisoprene at 70.4 °C. The increase in Dself with increasing solvent volume fraction could be described by the Fujita-Doolittle theory which states that the rate of self-diffusion scales with the free volume which in turn increases linearly with temperature. At higher solvent volume fractions the rate of selfdiffusion deviates from the Fujita-Doolittle theory, as the entanglement density decreased below the critical value. 

In Chapter 1, the assumption that gases and gas mixtures behave ideally at low pressures (1 bar and below) was stated. (Deviation from this with large amounts of readily condensable vapours under compression near atmospheric pressure was dealt with in Chapter 3.) The ideal gas equation, expressing the relationship between the variables pressure, volume, temperature and amount (number of moles) of gas, together with the expression of pressure in terms of particle number density (n) and Dalton s law of partial pressures, allow many calculations useful to vacuum technology to be carried out (Examples... 

Two models are available for interpreting attenuation spectra as a PSD in suspensions with chemically distinct, dispersed phases using the extended coupled phase theory.68 Both models assume that the attenuation spectrum of a mixture is composed of a superposition of component spectra. In the multiphase model, the PSD is represented as the sum of two log-normal distributions with the same standard deviation, that is, a bimodal distribution. The appearance of multiple solutions is avoided by setting a common standard deviation to the mean size of each distribution. This may be a poor assumption for the PSD (see section 11.3.2). The effective medium model assumes that only one target phase of a multidisperse system needs to be determined, while all other phases contribute to a homogeneous system, the so-called effective medium. Although not complicated by the possibility of multiple solutions, this model requires additional measurements to determine the density, viscosity, and acoustic attenuation of the effective medium. The attenuation spectrum of the effective medium is modeled via a polynomial fit, while the target phase is assumed to have a log-normal PSD.68 This model allows the PSD for mixtures of more than two phases to be determined. 

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