Multiphase thermodynamics

The Important conclusion is that complex controlling processes can occur in solubility phenomena in mixed electrolyte solutions. This is especially true of surface coatings formed kinetically or by multistate thermodynamics and which prevent the aqueous solution from interaction with internal bulk phases. One should remember of course that, when the degree of supersaturation is large enough for bulk precipitation to occur, the kinetic and multiphase thermodynamic processes studied above will apply to the actual bulk phases. 

Bennethum, L.S. and Cushman, J.H. (2002) Multicomponent, multiphase thermodynamics of swelling porous media with electroquasistatics I. Macroscale field equations, Transport in Porous Media, 47(3), 309-336... 

The multiphase thermodynamic model described above has been implemented as a computational tool using the ChemSheet thermodynamic software (part of the widely used Solgasmix/ChemSage/ChemApp program family) that supports the use of the Pitzer formalism in describing ionic interactions in solutions and a number non-ideal solution models for solid phases. Despite the fact that the thermodynamic... 

Multiphase Thermodynamics of Pulp Suspensions Table 2 Data input for the ESA and TMP models... 

In this chapter we look at the basic relationships between COj in natural waters that are important in the environment and also investigate CO2 utihzing processes in the environment. As an example of natural systems we consider a boreal low mineral lake and discuss the effects of acidification of aquatic ecosystems in context of multiphase thermodynamics. 

Scheme 6. The effect of COj partial pressure on the solubility of saturated calcite solution with and without added common-ion salt. The multiphase thermodynamic model allows the determination of the solubUities of carbonates in different p(CO )s.

This very brief review of phase equilibrium gives the reader the principles for dealing with two-phase systems. More background on the thermodynamic equilibrium of multiphase systems will sometimes be needed it is not covered in this book. The reader is advised to consult a multiphase thermodynamics book for that purpose. 

Bermethum LS, Cushman ]H (2002b) Multicomponent, multiphase thermodynamics of swelling... 

Statistical thermodynamics already provide an excellent framework to describe and model equilibrium properties of molecular systems. Molecular interactions, summarized for instance in terms of a potential of mean force, determine correlation functions and all thermodynamic properties. The (pair) correlation function represents the material structure which can be determined by scattering experiments via the scattering function. AU macroscopic properties of pure and mixed fluid systems can be derived by weU-estabhshed multiphase thermodynamics. In contrast, a similar framework for particulate building blocks only partly exists and needs to be developed much further. Besides equibbrium properties, nonequilibrium effects are particularly important in most particulate systems and need to be included in a comprehensive and complete picture. We will come back to these aspects in Section 4. 

Modem scaling theory is a quite powerful theoretical tool (appHcable to Hquid crystals, magnets, etc) that has been well estabUshed for several decades and has proven to be particularly useful for multiphase microemulsion systems (46). It describes not just iuterfacial tensions, but virtually any thermodynamic or physical property of a microemulsion system that is reasonably close to a critical poiat. For example, the compositions of a microemulsion and its conjugate phase are described by equations of the foUowiug form ... 

The foUowiag criterion of phase equUibrium can be developed from the first and second laws of thermodynamics the equUibrium state for a closed multiphase system of constant, uniform temperature and pressure is the state for which the total Gibbs energy is a minimum, whence... 

Flows are typically considered compressible when the density varies by more than 5 to 10 percent. In practice compressible flows are normally limited to gases, supercritical fluids, and multiphase flows containing gases. Liquid flows are normally considerea incompressible, except for certain calculations involved in hydraulie transient analysis (see following) where compressibility effects are important even for nearly incompressible hquids with extremely small density variations. Textbooks on compressible gas flow include Shapiro Dynamics and Thermodynamics of Compre.ssible Fluid Flow, vol. 1 and 11, Ronald Press, New York [1953]) and Zucrow and Hofmann (G .s Dynamics, vol. 1 and 11, Wiley, New York [1976]). 

For the analysis heat and mass transfer in concrete samples at high temperatures, the numerical model has been developed. It describes concrete, as a porous multiphase system which at local level is in thermodynamic balance with body interstice, filled by liquid water and gas phase. The model allows researching the dynamic characteristics of diffusion in view of concrete matrix phase transitions, which was usually described by means of experiments. 

One practical problem of the determinant method is the common unavailability of thermodynamic data and phase diagrams for multiphase compounds. For practical applications, an estimate obtained from data for binary compounds of the multinary system may be useful. 

Peles YP, Yarin LP, Hetsroni G (2000) Thermodynamic characteristics of two-phase flow in a heated capillary. Int J Multiphase Flow 26 1063-1093 Peles YP, Yarin LP, Hetsroni G (2001) Steady and unsteady flow in a heated micro-channels. Int J Multiphase Flow 28 1589-1616... 

We have considered thermodynamic equilibrium in homogeneous systems. When two or more phases exist, it is necessary that the requirements for reaction equilibria (i.e., Equations (7.46)) be satisfied simultaneously with the requirements for phase equilibria (i.e., that the component fugacities be equal in each phase). We leave the treatment of chemical equilibria in multiphase systems to the specialized literature, but note that the method of false transients normally works quite well for multiphase systems. The simulation includes reaction—typically confined to one phase—and mass transfer between the phases. The governing equations are given in Chapter 11. 

Traditional solid-state synthesis involves the direct reaction of stoichiometric quantities of pure elements and precursors in the solid state, at relatively high temperatures (ca. 1,000 °C). Briefly, reactants are measured out in a specific ratio, ground together, pressed into a pellet, and heated in order to facilitate interdiffusion and compound formation. The products are often in powdery and multiphase form, and prolonged annealing is necessary in order to manufacture larger crystals and pure end-products. In this manner, thermodynamically stable products under the reaction conditions are obtained, while rational design of desired products is limited, as little, if any, control is possible over the formation of metastable intermediates. ... 

The rates of multiphase reactions are often controlled by mass tran.sfer across the interface. An enlargement of the interfacial surface area can then speed up reactions and also affect selectivity. Formation of micelles (these are aggregates of surfactants, typically 400-800 nm in size, which can solubilize large quantities of hydrophobic substance) can lead to an enormous increase of the interfacial area, even at low concentrations. A qualitatively similar effect can be reached if microemulsions or hydrotropes are created. Microemulsions are colloidal dispersions that consist of monodisperse droplets of water-in-oil or oil-in-water, which are thermodynamically stable. Typically, droplets are 10 to 100 pm in diameter. Hydrotropes are substances like toluene/xylene/cumene sulphonic acids or their Na/K salts, glycol.s, urea, etc. These. substances are highly soluble in water and enormously increase the solubility of sparingly. soluble solutes. 

Agee, L. J., S. Banerjie, R. B. Duffey, and E. D. Hughes, 1978, Some Aspects of Two-Phase Models for Two-Phase Flow and Their Numerical Solutions, in Transient Two-Phase Flow, Proc. 2nd Specialists Meeting, OECD Committee for the Safety of Nuclear Installations, Paris, Vol. 1, pp. 27-58. (3) Ahmadi, G., and D. Ma, 1990, A Thermodynamical Formulation for Disposed Multiphase Turbulent Flows I. Basic Theory, Int. J. Multiphase Flow 16 323. (3)... 

There has been extensive progress made in the past several years in the formulation of statistical thermodynamics of mixtures and transport phenomena modeling of multiphase flow in composite media. This knowledge may now be applied to the understanding and prediction of the phase and transport behavior of reservoir fluids and other... 

In part II of the present report the nature and molecular characteristics of asphaltene and wax deposits from petroleum crudes are discussed. The field experiences with asphaltene and wax deposition and their related problems are discussed in part III. In order to predict the phenomena of asphaltene deposition one has to consider the use of the molecular thermodynamics of fluid phase equilibria and the theory of colloidal suspensions. In part IV of this report predictive approaches of the behavior of reservoir fluids and asphaltene depositions are reviewed from a fundamental point of view. This includes correlation and prediction of the effects of temperature, pressure, composition and flow characteristics of the miscible gas and crude on (i) Onset of asphaltene deposition (ii) Mechanism of asphaltene flocculation. The in situ precipitation and flocculation of asphaltene is expected to be quite different from the controlled laboratory experiments. This is primarily due to the multiphase flow through the reservoir porous media, streaming potential effects in pipes and conduits, and the interactions of the precipitates and the other in situ material presnet. In part V of the present report the conclusions are stated and the requirements for the development of successful predictive models for the asphaltene deposition and flocculation are discussed. 

The two main assumptions underlying the derivation of Eq. (5) are (1) thermodynamic equilibrium and (2) conditions of constant temperature and pressure. These assumptions, especially assumption number 1, however, are often violated in food systems. Most foods are nonequilibrium systems. The complex nature of food systems (i.e., multicomponent and multiphase) lends itself readily to conditions of nonequilibrium. Many food systems, such as baked products, are not in equilibrium because they experience various physical, chemical, and microbiological changes over time. Other food products, such as butter (a water-in-oil emulsion) and mayonnaise (an oil-in-water emulsion), are produced as nonequilibrium systems, stabilized by the use of emulsifying agents. Some food products violate the assumption of equilibrium because they exhibit hysteresis (the final c/w value is dependent on the path taken, e.g., desorption or adsorption) or delayed crystallization (i.e., lactose crystallization in ice cream and powdered milk). In the case of hysteresis, the final c/w value should be independent of the path taken and should only be dependent on temperature, pressure, and composition (i.e.,... 

In conclusion, the combination of thermodynamic measurements over single phase and multiphase regimes and kinetic measurements within single phase regions provides a comprehensive overall picture of the electrode performance. The extracted thermodynamic and kinetic data may be converted into the rate constants that describe the growth of new phases in the electrode during the course of discharge. 

The mathematical basis of classic thermodynamics was developed by J. Willard Gibbs in his essay [1], On the Equilibrium of Heterogeneous Substances, which builds on the earlier work of Kelvin, Clausius, and Helmholtz, among others. In particular, he derived the phase mle, which describes the conditions of equilibrium for multiphase, multicomponent systems, which are so important to the geologist and to the materials scientist. In this chapter, we will present a derivation of the phase rule and apply the result to several examples. 

Although we have indicated some applications of thermodynamics to biological systems, more extensive discussions are available [6]. The study of equilibrium involving multiple reactions in multiphase systems and the estimation of their thermodynamic properties are now easier as a result of the development of computers and appropriate algorithms [7]. 

It is the intent of this doeument to define the terms most commonly encountered in the field of polymer blends and eomposites. The scope has been limited to mixtures in which the eomponents differ in ehemical composition or molar mass or both and in which the continuous phase is polymeric. Many of the materials described by the term multiphase are two-phase systems that may show a multitude of finely dispersed phase domains. Hence, incidental thermodynamic descriptions are mainly limited to binary mixtures, although they can be and, in the scientific literature, have been generalized to multicomponent mixtures. Crystalline polymers and liquid-crystal polymers have been considered in other documents [1,2] and are not discussed here. 

Capability of a mixture to exist for an indefinite period of time as a single phase that is separated by a small or zero energy barrier from a thermodynamically more stable multiphase system [3]. 

For thermodynamic reasons mixability may be all right, but the last step in a mixing process, when the droplets are snflrciently small, is a diffusion process this needs a considerable time, which is not always available in a blending process (in this way a "multiphase" blend conld be formed, see MT Fignre 9.4.d)... 

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