Two-phase existence

There has been renewed interest over the last few years in erosion-corrosion, i.e. essentially velocity-assisted corrosion since it appeared in the feed systems of certain nuclear plant. This prompted extensive experimental investigations . Erosion-corrosion is influenced by many factors-chemistry, flow, temperature, heat flux, and whether one or two phases exist. It also varies with the material, resistance increasing from mild steel, through 1% Cr-Mo to 2% Cr-Mo. 

Upon substitution into either one of the equations of stability [Eq. (98) or (99)], we can then determine whether the gas mixture exists in one or two stable phases. If two phases exist at some temperature and pressure, we can calculate the two phase compositions by utilizing the two equilibrium relations... 

The number of phases is the number of different homogeneous regions in the system. Thus, in a system containing liquid water and several chunks of ice, only two phases exist. The number of degrees of freedom is the number of intensive variables that can be altered freely without the appearance or disappearance of a phase. First we wUl discuss a system that does not react chemically, that is, one in which the number of components is simply the number of chemical species. 

Two-Phase theory of Davidson According to the two-phase theory, two phases exist in the bubbling fluidized bed (a) the bubbling phase consisting of gas bubbles, and (b) the particulate phase, namely the solids around the bubbles. The particulate phase is alternatively called the emulsion phase. Bubbles stay in the bubble phase and penetrate only a small distance into the emulsion phase. This zone of penetration is called cloud since it envelops the rising bubble. 

Any system in. which two phases exist. In. the context of relief system sizing, a two-phase system usually comprises a gas/ vapour phase and a liquid phase. 

The distillation technique is not used to separate complex mixtures, but finds its acceptance more for the preparation of large quantities of pure substances or the separation of complex mixtures into fractions. The technique depends on the distribution of constituents between the liquid mixture and component vapors in equilibrium with the mixture two phases exist because of the partial evaporation of the liquids. How effective the distillation becomes depends upon the type equipment employed, the method of distillation, and the properties of the mixture components. The distinguishing aspects of distillation and evaporation are that in the former all components are volatile, whereas in the latter technique volatile components are separated from nonvolatile components. An example of distillation would be the separation of ethyl alcohol and benzene. An evaporative separation would be the separation of water from an aqueous solution of some inorganic salt, for example, sodium sulfate. 

At temperatures and pressures between those of the bubblepoint and dewpoint, a mixture of two phases exists whose amounts and compositions depend on the conditions that are imposed on the system. The most common sets of such conditions are fixed T and P, or fixed H and P, or fixed S and P. Fixed T and P will be considered first. 

The combined effect of disorder and the lattice potential on the zero temperature phase diagram, i.e., the competition between unpinning (Anderson) and lock-in (Mott) transition, is still controversially discussed [41, 14] and cannot be explained by the RG-results presented here, since both perturbations become relevant for small K. However, using Imry-Ma arguments one finds, that as soon as If is below one of the two critical values (for the unpinning and lock-in transition) the disorder dominates the lattice potential and only two phases exist. This is in contrast to the proposed existence of a so-called intermediate Mott- Glass phase [14]. 

Two phases exist in the activated sludge reactor the liquid phase consists of water, soluble ions and soluble substrate while the solid phase (biomass or sludge) has setdeable waste materials, dead and alive MOs in it. Metals associated with these phases were investigated in this study. The material balance for the metals at the steady state is defined as follows ... 

The phase equilibrium of the binary system stearyl alcohol/C02 was measured in a high pressure view cell (own design) according to the synthetic method by Teipel et al. [6] and presented in Fig. 2. The curves represent the border between the homogeneous and two phase region above the curve a homogeneous solution is present, below two phases exist. The measurements were carried out for different concentrations of stearyl alcohol in CO2 represented by the different curves. It is seen that 2.1 wt.% of stearyl alcohol are complete soluble in SC-CO2 at 333 K and 20 MPa. 

We must emphasize that these conditions are valid only when the standard state of a component is the same for both phases. We now choose a temperature, calculate values of Aju and Aju for each phase for various mole fractions and plot Aju against Aju for each phase. Two curves are obtained, one for each phase. The point of intersection of the curves gives the equilibrium values of Aju and Aju according to Equations (10.199) and (10.200). The calculation of x1 by the use of the left-hand side of Equation (10.198) and zl by the use of the right-hand side of Equation (10.198) is then relatively simple. If no intersection occurs, then no equilibrium between the two phases exists at the chosen temperature and pressure. The calculation must be repeated for each temperature. Activities could be used in place of Apu provided the same standard state for a component is used for both phases. 

One of the simplified heat transfer models of two-phase flows is the pseudocontinuum one-phase flow model, in which it is assumed that (1) local thermal equilibrium between the two phases exists (2) particles are evenly distributed (3) flow is uniform and (4) heat conduction is dominant in the cross-stream direction. Therefore, the heat balance leads to a single-phase energy equation which is based on effective gas-solid properties and averaged temperatures and velocities. For an axisymmetric flow heated by a cylindrical heating surface at rw, the heat balance equation can be written as... 

Note that when two phases exist both x and > i are independent of z. ... 

For mixtures, the phase envelopes expand from a curve to a region for the single component. Recall that in order for a single component to exist in two phase (vapor + liquid), the conditions had to fall exactly on the vapor pressure curve. For a mixture, there is a region over the pressure-temperature plane where two phases exist. 

A. Stage 1 Properties, if Two Phases Exist the Theory of Melting and Freezing of Microclusters... 

In a two-phase vapor-liquid mixture at equilibrium, if all the components can vapor- ize and condense, a component in one phase is in equilibrium with the same compo-nent in the other phase. The equilibrium relationship depends on the temperature and pressure, and perhaps composition, of the mixture. Figure 3.15 illustrates two cases, one at constant pressure and the other at constant temperature. At the pairs of points A and B, and C and D, the respective pure components exert their respective vapor pressures at the equilibrium temperature. In between the pairs of points, as the overall composition of the mixture changes, two phases exist, each having a different composition for the same component as indicated by the dashed lines. Two useful linear ( ideal ) equations exist to relate the mole fraction of one component in the vapor phase to the mole fraction of the same component in the liquid phase. 

Since all points on a tie line have the same temperature, pressure, component concentration in one phase, and component concentration in the other phase, one more variable must be specified to define the relative amounts of the phases at equilibrium. The specihed variable could itself be either the fraction of one phase out of the total or the mixture composition. Note that only two component concentrations are independent in a ternary. In the single-phase region there are four degrees of freedom according to the phase rule. Therefore, if the fraction of one phase or whether one or two phases exist is unknown, four independent variables must be specihed to completely dehne the system. 

When two phases exist in a specimen, the resultant thermal conductivity is calculated by the following equation[6],... 

A second is hydrostatic tank gauging, where level is inferred from pressure. Again, density, particularly if two phases exist (aqueous and foam), may render this approach questionable. 

A first step rules out a two-phase existence for all those components whose critical temperatures are lower than that of the mixture. When the latter is lower, the component could conceivably exist in two phases. In the cases encountered by the author, the number of potential two-phase components was normally one or two and exceptionally as high as four. These cases were analyzed as follows ... 

If the temperature is raised to Tj, the phase behavior shown in figure 3.7e occurs. This temperature is greater than the UCEP temperature, therefore two phases exist as the pressure is increased as long as the critical mixture curve is not intersected. The two branches of the vapor-liquid phase envelope approach each other in composition at an intermediate pressure and it appears that a mixture critical point may occur. But as the pressure is further increased, a mixture critical point is not observed and the two curves begin to diverge. To avoid confusion, the phase behavior shown in figure 3.7e is not included in the P-T-x diagram. 

---