Equation for mixtures

One can effectively reduce the tliree components to two with quasibinary mixtures in which the second component is a mixture of very similar higher hydrocarbons. Figure A2.5.31 shows a phase diagram [40] calculated from a generalized van der Waals equation for mixtures of ethane n = 2) with nomial hydrocarbons of different carbon number n.2 (treated as continuous). It is evident that, for some values of the parameter n, those to the left of the tricritical point at = 16.48, all that will be observed with increasing... 

In addition to the experimental results of phase equilibria, the correlation with the widely known GE models was assigned to. It was indicated by many authors that SLE, LLE, and VLE data of ILs can be correlated by Wilson, NRTL, or UNIQUAC models [52,54,64,79,91-101,106,112,131,134]. For the LLE experimental data, the NRTL model is very convenient, especially for the SLE/LLE correlation with the same binary parameters of nonrandom two-liquid equation for mixtures of two components. For the binary systems with alcohols the UNIQUAC equation is more adequate [131]. For simplicity, the IL is treated as a single neutral component in these calculations. The results may be used for prediction in ternary systems or for interpolation purposes. In many systems it is difficult to obtain experimentally the equilibrium curve at very low solubilities of the IL in the solvent. Because this solubility is on the level of mole fraction 10 or 10 , sometimes only... 

Cancer risk equation for mixtures Riskx = ERiski,... 

Example 7.3 Total energy flow and phenomenological equations For mixtures, the energy flow contains the conductive flow qc, and the contributions resulting from the interdiffusion q, of various substances and the Dufour effect q we therefore express the total energy flow relative to the mass-average velocity... 

G. The Mofiitt Equation for Mixtures of Helices and Random Coils.462... 

Kubaczka A. and Bandrowski, J., Solutions of a System of Multicomponent Mass Transport Equation for Mixtures of Real Fluids, Chem. Eng. Sci., 46, 539-556 (1991). 

Note that the momentum and energy equations for mixtures and pure fluids differ in their last terms (e.g., [11] [12] [13] [169]), where pg has been replaced by X)c=if cgc in the momentum equation and p(g v) has been replaced by Pc(gc Vc) in the energy equation, respectively. In the mixture equations account are taken of the fact that each chemical species present may be acted on by a different external force per unit mass gc. 

Using Excel solver for solving simultaneous equations for mixture absorbances (Example 16.5) ... 

Be able to use the mass, energy, and entropy balance equations for mixtures (Secs. 

To derive the macroscopic entropy balance equation for mixtures we now %t. d — S, in Eq. 2.1-4 and make the same identification for the entropy flow terms as was made in Sec. 4.1, to obtain... 

Adelman has shown that (5.6a), the OZ equation for mixtures, can be transformed into an effective OZ equation that can be written in the form... 

Approximation equation for mixtures of acids and bases. Explicit equation for [H+] in simple cases... 

Mixture properties are predicted from Equation 21 by using the hard-sphere equation for mixtures and using pseudo criticals to evaluate pk from known values of it for the reference. 

In this study the BWR-Starling (BWR-S) (20,21) equation of state was used, primarily because it has been fitted to a wide range of pure components. For some components there are other equations which represent isochoric behavior much better. However, the effect of the HSE procedure for mixtures when pure-component equations of state are known is to generate a more rigorous composition dependence in the reference-fluid equation of state. The BWR-S equation for mixtures has an empirical composition dependence which works well in some cases, particularly for hydrocarbon mixtures, but not so well for others, especially when nonhydrocarbons are involved. When the BWR-S equation is used for all pure component properties, it is interesting to compare the theoretically based composition dependence induced by the HSE theory with its empirical form in the BWR-S mixture equation. 

If the R-K equation of state is substituted into (4-50), the required integration is performed as shown in detail by Edmister, and the result is substituted into (4-61) and (4-62), the equations for mixture molal enthalpy... 

The structure of this chapter is as follows. First, the results obtained for individual surfactant solutions are presented, which are preceded, for the sake of convenience, by a summary of the main equations corresponding to the various theoretical models discussed in Chapter 2. The software used for fitting the models to experimental data will be described in Chapter 7. Then, surfactant mixtures are considered with a number of experimental and theoretical examples. A summary of the main theoretical equations for mixtures of ionic and non-ionic surfactants (the corresponding fitting software again is described in Chapter 7). Also some approximate theoretical models for the mixture of two or more surfactants is presented and compared with experimental results. 

Write ionic equations for mixtures of aqueous solutions. 

Adkins, J.E. Non-Unear diffusion, II constitutive equations for mixtures of isotropic fluids. Phil. Trans. R. Soc. Lond. A255,635-648 (1963)... 

By using arguments quite similar to those presented in Section IV.B, we derive constituent balance equations for mixture. 

These relations are fundamental in obtaining the local form of constituent balance equations for mixture. In order to derive them, we can use Table 10.2 for a constituent of mixture. In this way, we obtain the following. 

For reprocessed uranium, Aj values may be calculated by using the equation for mixtures in para. 404 and taking account of the physical and chanical characteristics likely to arise in both normal and accident conditions. It may also be possible to demonstrate that the value is unlimited by showing that 10 mg of the uranium will have less activity than that giving rise to a committed effective dose of 50 mSv for that mixture. In addition, for calculating Aj values in the case of reprocessed uranium, the advice given in Ref. [8] may provide useful information. 

The equations for mixtures additionally contain the mole numbers, that is, the composition as a variable. They are valid for both vapor and liquid. With the help of these equations, the fugacity coefficient can be determined from experimental PvT Xi(yi) data or it can be calculated using an equation of state. ... 

This book contains correlated vapor-liquid-equilibrium data on mixtures (mostly binary but with some multicomponent systems). The correlations are done using any one of several approaches The Antoine equation for a pure component, van Laar and Margules equations for mixtures. In all cases the source(s) of the experimental data is given. The coverage of systems ( 400)... 

Mixture of Anionic Surfactants onto Alumina. Most EOR surfactants are mixtures of isomers, but these mixtures are too complex for application of basic theory. In contrast, the effectiveness of ideal solution theory in explaining region II adsorption for binary mixtures of anionic surfactants has been demonstrated [5Jj. These controlled isomeric mixtures allow application of the ideal solution theory. The application of this theory utilized a reduced adsorption equation for mixtures of anionic surfactants [52]. The parameters for this reduced... 

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