Component critical volumes

For dilute solutions, the ratio of qx to q2 is given by the ratio of the pure-component critical volumes. This limiting relationship is somewhat arbitrary and is chosen primarily for convenience any other convenient measure of molecular size could be used—for example, van der Waals b or Lennard-Jones a3. 

In this work component critical volumes were taken from Reid et al. (23). They are given in Table VI, along with root mean square deviations between the correlation predictions and the isothermal compressibilities tabulated in Appendix A of Reference 11 (pressures up to 50 MPa). For Ar, CH4, and C2HG the correlation is quite accurate, giving isothermal compressibilities with average deviations within 5%. Deviations for N2 are on this order for 91 and 100 K, but they become... 

Table VI. Component Critical Volumes (Vc) from Reference 23 and Root Mean Square Deviations (s) between the Brelvi—O Connell Correlation (12) and Component Isothermal Compressibilities from Reference 11, pp. 124—128...

Basic pure component constants required to characterize components or mixtures for calculation of other properties include the melting point, normal boiling point, critical temperature, critical pressure, critical volume, critical compressibihty factor, acentric factor, and several other characterization properties. This section details for each propeidy the method of calculation for an accurate technique of prediction for each category of compound, and it references other accurate techniques for which space is not available for inclusion. 

Ten is the mixture critical temperature in K. is the critical volume of a component, mVkmole. The mole frac tion of a component is y. The mixture contains i components. 

Hydraulic resistance of membrane Velocity of i th component, cm/sec Critical volume fraction... 

Table 1 gives the components present in the crude DDSO and their properties critical pressure (Pc), critical temperature (Tc), critical volume (Vc) and acentric factor (co). These properties were obtained from hypothetical components (a tool of the commercial simulator HYSYS) that are created through the UNIFAC group contribution. The developed DISMOL simulator requires these properties (mean free path enthalpy of vaporization mass diffusivity vapor pressure liquid density heat capacity thermal conductivity viscosity and equipment, process, and system characteristics that are simulation inputs) in calculating other properties of the system, such as evaporation rate, temperature and concentration profiles, residence time, stream compositions, and flow rates (output from the simulation). Furthermore, film thickness and liquid velocity profile on the evaporator are also calculated. 

All work reviewed so far in this subsection concerns thin films with neutral surfaces, but we feel that the general scaling description Eqs. (129)-(133), Fig. 23) should also apply to thin films with symmetric surfaces that both favor the same component (say B, cf. Fig. 5) relative to the other. The additional feature, not present in Fig. 22, then is a shift of the critical volume fraction critCD) with thickness. Scaling considerations [216,224,225] predict for this shift... 

Calculate the volume using Kay s method. In this method, V is found from the equation V = ZRT/P, where Z, the compressibility factor, is calculated on the basis of pseudocritical constants that are computed as mole-fraction-weighted averages of the critical constants of the pure compounds. Thus, T = Z K, 71, and similarly for Pc and Z, where the subscript c denotes critical, the prime denotes pseudo, the subscript i pertains to the ith component, and Y is mole fraction. Pure-component critical properties can be obtained from handbooks. The calculations can then be set out as a matrix ... 

This problem can be initially overcome using a volume ratio instead of a lattice site ratio, expressing the percolation thresholds as critical volume fractions [36, 4(M2], Nevertheless, the influence of the particle size of the components on the percolation threshold cannot be explained using a volume fraction that is, from this point of view, tablets with the same excipient volume are equivalent independent of their particle size. A first qualitative study of the influence of particle size on the percolation threshold [43] demonstrated that this is in clear disagreement with experimental data. 

X (z) t b c cD mean area per chain comprising brush layer 4.1 local volume fraction of blend component A at depth z 2.1 local composition with plateau in ( >(z) profile 3.2.1 critical volume fraction 2.1 critical volume fraction of very thin film between symmetric walls 3.2.2 ... 

Table 2 shows the pure component properties of all the substances involved in this study. Here, M is the molecular weight, Tj. is the critical temperature, 7], is the normal boiling temperature, is the critical pressure, Vc is the critical volume, and w is the acentric factor. Data were obtained from Diadem Public [17]. 

Ki = ratio of vapor mole fraction to liquid mole fraction of Component i for vapor and liquid in equilibrium P = system pressure Pc, = critical pressure of Component i R = gas constant T = system temperature V = system volume Vc = critical volume... 

An equation of state is used to calculate V and the V values, and the excess volume is then obtained from Equation 1. For practical applications, VE from the equation of state must be combined with known component molar volumes to obtain the mixture molar volume. The hope is that, due to a cancellation of errors, much simpler equations of state can be used to accurately describe VE(P, T, x) than would be necessary to yield directly V(P, T, x) to the required accuracy. The VE method is only of practical use when the temperature of the solution is below the critical temperatures of the major components. 

The equation of state uses corresponding states theory to determine the attractive and volume parameters of each species. Therefore, the pure component critical temperature, 7, and critical pressure, are required. The EOS uses a third parameter, viz. Pitzer s acentric factor, (O, (9)... 

Because the modulus of fibers is usually much higher than that of the matrix, the load on a composite will therefore be carried mostly by its fiber component (see Example 3.4). However, a critical volume fraction of fibers ( crit) is required to realize matrix retnforcemenL Thus for Equation 3.127 and Equation 3.130 to be valid, 0f > cnt-... 

Critical Volume of Pure Components.—The critical volume is the most difficult of the three critical constants to measure and consequently critical volumes are rarely measured to an accuracy of better than 0.5 per cent. The best method is to measure orthobaric liquid and gas densities up to within a kelvin or so of the critical temperature. The critical density is obtained using the law of rectilinear diameters, i.e. by extrapolating the mean of these densities to the critical temperature. This technique was originally proposed by Cailletet and Mathias and has been investigated carefully by Schneider and co-workers and discussed in detail by Rowlinson. ... 

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