Liquid phases calculations

Assuming ideal mixing for both gas and liquid phases, calculate ... 

In the liquid phase, calculations of the pair correlation functions, dielectric constant, and diffusion constant have generated the most attention. There exist nonpolarizable and polarizable models that can reproduce each quantity individually it is considerably more difficult to reproduce all quantities (together with the pressure and energy) simultaneously. In general, polarizable models have no distinct advantage in reproducing the structural and energetic properties of liquid water, but they allow for better treatment of dynamic properties. 

Liquid Phase Calculations of the Linear Response. The data in Table 5 for the isotropic polarizability, derived formally via the Lorentz-Lorenz equation (1) from the measured refractive index, shows that the assumption that individual molecular properties are largely retained at high frequency in the liquid is very reasonable. While the specific susceptibilities for the gas and liquid phases differ, once the correction for the polarization of the surface of a spherical cavity, which is the essential feature of the Lorentz-Lorenz equation, has been applied, it is clear that the average molecular polarizabilities in the gas and liquid have values which always agree within 5 or 10%. 

As a starting point, the liquid can be taken to be water that has equilibrated with air to obtain its noble gas content. Furthermore, it is assumed that the liquid is saturated with respect to the dominant gas species forming the bubble/gas phase. The column is divided into cells and it is assumed that there is no transport of dissolved gases or fluid between the cells. When a gas bubble, initially with no noble gas content, is introduced into the first cell the distribution of both Ne and Ar can be calculated from Equation (16) assuming complete equilibration between the gas and fluid in that cell only. The volume of the bubble is assumed to be constant and, now with a noble gas content, is moved to the next cell. Equilibrium is again assumed, and the resulting distribution of Ne and Ar between the gas and liquid phases calculated. In this manner the Ne and Ar concentrations and Ne/Ar ratio can be calculated for the gas phase and each water cell as the bubble is sequentially passed through the unit cells of the liquid column. 

The content of clinker melt is increasing with temperature, and its viscosity is decreasing. The content of hqnid phase at chosen temperature (compare with Sect. 2.2) can be calculated from corresponding multicomponent systems. Lea and Parker [24] gave the simplified formnlae, which permit the content of liquid phase calculation ... 

Fig. 6 Relation between the silica modulus and the content of clinker liquid phase, calculated according to L. A. Dahl, at a clinkering temperature of 1450° C (from Locher, 1979)...

There is one more reason, if the first one is not responsible for the deviations. This is the accuracy of the temperature dependences of the heat capacity Cp of the solid and liquid phases. Calculations show that, for instance, a 10% error in the temperature dependence for liquid copper toward an increase in its heat capacity results in a noticeable (by about 50 K) shift of the calculated film thickness dependence of melting temperature toward lower temperatures. 

In this paper we review a recently developed theoretical method for phase equilibrium calculation which explicitly accounts for strongly orientation-dependent forces. These anisotropic forces are taken into account through a perturbation scheme in which the reference fluid is composed of simple spherical molecules in practice, the known properties of argon, or those of a Lennard-Jones fluid simulated on the computer, may be used. Such a perturbation scheme was first suggested by Pople ( 7) more than twenty years ago, but was not Immediately used for liquid phase calculations because the reference fluid properties were not sufficiently well known. Since 1972 the theory has been extended and improved, and its successful application to liquids of strongly polar or quadrupolar molecules dates from 1974 ( 7) ... 

At the furnace outlet conditions of temperature and pressure, find the volume percent vaporized as Point 1 on Figure 2.12. From crude assay data, calculate the weight of the vaporized crude. Using the weight of the vapor and liquid phases, calculate the heat content of the mixture leaving the furnace as... 

Froude number for the liquid phase, calculated with S ... 

Reynolds number for the liquid phase calculated with dp and... 

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