Solid liquid nonideal systems

There are many types of phase diagrams in addition to the two cases presented here these are summarized in detail by Zief and Wilcox (op. cit., p. 21). Solid-liquid phase equilibria must be determined experimentally for most binary and multicomponent systems. Predictive methods are based mostly on ideal phase behavior and have limited accuracy near eutectics. A predictive technique based on extracting liquid-phase activity coefficients from vapor-liquid equilibria that is useful for estimating nonideal binary or multicomponent solid-liquid phase behavior has been reported by Muir (Pap. 71f, 73d ann. meet., AIChE, Chicago, 1980). 

The case of binary solid-liquid equilibrium permits one to focus on liquid-phase nonidealities because the activity coefficient of solid component ij, Yjj, equals unity. Aselage et al. (148) investigated the liquid-solution behavior in the well-characterized Ga-Sb and In-Sb systems. The availability of a thermodynamically consistent data base (measurements of liquidus, component activity, and enthalpy of mixing) provided the opportunity to examine a variety of solution models. Little difference was found among seven models in their ability to fit the combined data base, although asymmetric models are expected to perform better in some systems. 

Two theoretical techniques worthy of serious review here, perturbation and Green function methods, can be considered complementary. Perturbation methods can be employed in systems which deviate only slightly from regular shape (mostly from planar geometry, but also from other geometries). However, they can be used to treat both linear and nonlinear PB problems. Green function methods on the other hand are applicable to systems of arbitrary irregularity but are limited to low surface potential surfaces for which the use of the linear PB equation is permitted. Both methods are discussed here with reference to surfactant solutions which are a potentially rich source of nonideal surfaces whether these be solid-liquid interfaces with adsorbed surfactants or whether surfactant self-assembly itself creates the interface. 

In general, the steps of this separations system synthesis method for nonideal mixtures involving azeotropes include examination of the RCM representation (overlaid with vapor-liquid equlibria (VLE) pinch information, liquid-liquid equlibria (LLE) binodal curves and tie lines, and. solid-liquid equlibria (SLE) phase diagrams if appropriate) determination of the critical thermodynamic features to be avoided (e.g., pinched regions), overcome (e.g., necessary distillation... 

Often solid-liquid equilibrium data are not available for the system of interest, and experimental determination of the solidus-liquidus curves is required. If the system of interest is simple (ie., two to three components) and well behaved (ideal), then reliable predictive methods are available. Techniques for predicting nonideal solid-liquid phase behavior and muWcomponent equilibria are emerging. 

In Fig. 9.26, the thermodynamic equilibrium, solid-liquid phase diagram of a binary (species A and B) system is shown for a nonideal solid solution (i.e., miscible liquid but immiscible solid phase). The melting temperatures of pure substances are shown with Tm A and Tm B. At the eutectic-point mole fraction, designated by the subscript e, both solid and liquid can coexist at equilibrium. In this diagram the liquidus and solidus lines are approximated as straight lines. A dendritic temperature T and the dendritic mass fractions of species (p)7(p)s and (p)equilibrium partition ratio kp is used to relate the solid- and liquid-phase mass fractions of species (p)7(p)J and (p)f/(p)f on the liquidus and solidus lines at a given temperature and pressure, that is,... 

Following Eq. (8.9) in the case of nonideal systems the knowledge about the real behavior (e.g., activity coefficients yi) both in the liquid and in the solid phase is required as additional information for the calculation of SLE. The deviation from ideal behavior can be taken into account using for example, g -models or equations of state. Starting from Eq. (8.9) for nonideal systems, the following expression is... 

Construct phase diagrams for binary systems in vapor-liquid equilibria (VLE), liquid-liquid equilibria (LLE), vapor-liquid-liquid equilibria (VLLE), solid-liquid equilibria (SLE), solid-solid equilibria (SSE), and solid-solid-liquid equilibria (SSLE), correcting for nonideal behavior in the vapor, liquid, or solid phases using fugacity coefficients and activity coefficients. 

Our treatment of Chemical Reaction Engineering begins in Chapters 1 and 2 and continues in Chapters 11-24. After an introduction (Chapter 11) surveying the field, the next five Chapters (12-16) are devoted to performance and design characteristics of four ideal reactor models (batch, CSTR, plug-flow, and laminar-flow), and to the characteristics of various types of ideal flow involved in continuous-flow reactors. Chapter 17 deals with comparisons and combinations of ideal reactors. Chapter 18 deals with ideal reactors for complex (multireaction) systems. Chapters 19 and 20 treat nonideal flow and reactor considerations taking this into account. Chapters 21-24 provide an introduction to reactors for multiphase systems, including fixed-bed catalytic reactors, fluidized-bed reactors, and reactors for gas-solid and gas-liquid reactions. 

Regarding this new edition first of all I should say that in spirit it follows the earlier ones, and I try to keep things simple. In fact, I have removed material from here and there that I felt more properly belonged in advanced books. But I have added a number of new topics—biochemical systems, reactors with fluidized solids, gas/liquid reactors, and more on nonideal flow. The reason for this is my feeling that students should at least be introduced to these subjects so that they will have an idea of how to approach problems in these important areas. 

Although modeling of supercritical phase behavior can sometimes be done using relatively simple thermodynamics, this is not the norm. Especially in the region of the critical point, extreme nonidealities occur and high compressibilities must be addressed. Several review papers and books discuss modeling of systems comprised of supercritical fluids and solid or liquid solutes (rl,r4—r7,r9,r49,r50). 

In addition to the physical state of reactants, it should be remembered that the ideal behavior is encountered only in the gaseous state. As the polymerization processes involve liquid (solution or bulk) and/or solid (condensed or crystalline) states, the interactions between monomer and monomer, monomer and solvent, or monomer and polymer may introduce sometimes significant deviations from the equations derived for ideal systems. The quantitative treatment of thermodynamics of nonideal reversible polymerizations is given in Ref. 54. 

Alternatively, Jaroniec and Martire have described liquid-solid chromatography in terms of classical thermodynamics (82). They show that a rigorous consideration of solute and solvent competitive adsorption in systems with a nonideal mobile phase and a surface-influenced nonideal stationary phase leads to a general equation for the distribution coefficient of a solute involving concurrent adsorption and partition effects. This equation is phrased in terms of interaction parameters and activity coefficients, which would need to be evaluated or estimated in actual applications. 

Besides the theoretical interest in the unusual phase behavior encountered in these systems, the principles involved can be applied in operations wherein the nonideality is intentionally created. The magnitude of solubility of a compound of low volatility in a gas above its critical temperature. .. is sufficient to consider the gas as an extracting medium, that is fluid-liquid or fluid-solid extraction analogous to liquid-liquid extraction and leaching. In this case the solute is removed and the solvent recovered by partial decompression. Thus compression of a gas over a mixture of compounds could selectively dissolve one compound, permitting it to be removed from the mixture. Partial decompression of the fluid elsewhere would drop out the dissolved compound, and the gas could be reused for further extraction. 

Flgare 1.5-2 shows exparimental and correlated binary VLE data for three dioxane-n-alkane systems at 80°C.m The pressure levels are modest (0.2-1.4 amt) liquid-phase nonidealities are sufficiently large to promote a2eotropy in all threa cases. Equations (1.5-12)—(1.5-15) were used for the data reduction, with experimental values for the Pf1 and virial coefficients were estimated from the correlation of Tsono-poulos.7 Activity coefficients were assumed to be represented by the three-parameter Margules equation, aed (he products of the data rednction were seis of valnes for parameters Al2, Ait. and D in Eqs. (1.4-10) and (1.4-11). The parameters so determined produce the correlations of the data shown by the solid curves in Fig. 1.5-2. For all threa systems, the data are represented to within their exparimental uncertainty. 

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