Equilibrium models for

Hoffman, M. R. (1981). Thermodynamic, kinetic and extra-thermodynamic considerations in the development of equilibrium models for aquatic systems. Environ. Sci. Technol. 15,345-353. 

Chan, M. Yen, T.F. A Chemical Equilibrium Model for Interfadal Activity of Crude Oil in Aqueous Alkaline Solution The Effects of pH, Alkali and Salt, Canadian J. Chem. Eng. 1982, 60, 305. 

Fein JB, Daughney CJ, Yee N, Davis TA (1997) A chemical equilibrium model for metal adsorption onto bacterial surfaces. Geochim Cosmochim Acta 61 3319-3328... 

The equilibrium model for the adsorption of polymers at solid-liquid interfaces recently presented by Hogg and Mirville (1) has been evaluated at some length. It has been shown that, for polymers consisting of a reasonably large number of segments, the adsorption isotherms can be closely approximated by an expression of the form ... 

Fig. 14. Axial channeling scans from Nielsen et al. (1988) showing the yield from the (3He, ap) reaction with 2H in B—H pairs and the Si crystal host dip. The solid lines show a fit to the experimental data with the Statistical Equilibrium model for 87% of the 2H in a near bond-center site and the remainder in a T site.

Greenberg, J. P. and N. Mpller, 1989, The prediction of mineral solubilities in natural waters, a chemical equilibrium model for the Na-K-Ca-Cl-S04-H20 system to high concentration from 0 to 250 °C. Geochimica Cosmochimica Acta 53,2503-2518. 

The material covered in the appendices is provided as a supplement for readers interested in more detail than could be provided in the main text. Appendix A discusses the derivation of the spectral relaxation (SR) model starting from the scalar spectral transport equation. The SR model is introduced in Chapter 4 as a non-equilibrium model for the scalar dissipation rate. The material in Appendix A is an attempt to connect the model to a more fundamental description based on two-point spectral transport. This connection can be exploited to extract model parameters from direct-numerical simulation data of homogeneous turbulent scalar mixing (Fox and Yeung 1999). 

A logical extension of the spectral equilibrium model for e would be to consider nonequilibrium spectral transport from large to small scales. Such models are an active area of current research (e.g., Schiestel 1987 and Hanjalic et al. 1997). Low-Reynolds-number models for e typically add new terms to correct for the viscous sub-layer near walls, and adjust the model coefficients to include a dependency on Re/,. These models are still ad hoc in the sense that there is little physical justification - instead models are validated and tuned for particular flows. 

Bhattacharyya, S. C. (1996). Applied general equilibrium models for energy studies a survey. Energy Economics, 18 (3), 145-164. 

Gunning, J. W. and Keyzer, M. A. (1995). Applied general equilibrium models for policy analysis. In Handbook of Development Economics, vol. 3A, pp. 2025-2107. 

The present paper deals with one aspect of this problem the calculation of phase separation critical points in reacting mixtures. The model employed is the Soave-Redlich-Kwong equation of state (1 ), which is typical of several equations of state (2, 5) which have relatively recently come into wide use as phase equilibrium models for light gas mixtures, sometimes including water and the acid gases as components (4, . 5, 6). If the critical point contained in the equation of state (perhaps even for the mixture at reaction equilibrium) can be found directly, the result will aid in other equilibrium computations. 

We now discuss in detail setting up the partial equilibrium model for a particular case. The dissolution of chalcopyrite, CuFeS2, has been studied extensively in the laboratory ( 3,4 5) and we have been interested in it because of its importance in dump leaching. Under dump leaching conditions, two dissolution reactions have been identified for this mineral (3,4 5) ... 

We have solved the equations of the partial equilibrium model for a number of different initial analytical concentrations... 

Explosive boiling is certainly not the normal event to occur when liquids are heated. Thus, the very rapid vaporization process must be explained by theories other than standard equilibrium models. For example, if two liquids are brought into contact, and one is relatively nonvolatile but at a temperature significantly above the boiling point of the second liquid, an explosive rapid-phase transition sometimes results. Various models have been proposed to describe such transitions. None has been... 

Polach, K.J. and Widom, J. (1995) Mechanism of protein access to specific DNA sequences in chromatin a dynamic equilibrium model for gene regulation. J. Mol. Biol. 254, 130-149. 

The threshold concentration of monomer that must be exceeded for any observable polymer formation in a self-assembling system. In the context of Oosawa s condensation-equilibrium model for protein polymerization, the cooperativity of nucleation and the intrinsic thermodynamic instability of nuclei contribute to the sudden onset of polymer formation as the monomer concentration reaches and exceeds the critical concentration. Condensation-equilibrium processes that exhibit critical concentration behavior in vitro include F-actin formation from G-actin, microtubule self-assembly from tubulin, and fibril formation from amyloid P protein. Critical concentration behavior will also occur in indefinite isodesmic polymerization reactions that involve a stable template. One example is the elongation of microtubules from centrosomes, basal bodies, or axonemes. 

By comparing the actual composition of sea water (sediments + sea -f- air) with a model in which the pertinent components (minerals, volatiles) with which water has come into contact are allowed to reach true equilibrium, Sillen in 1959 epitomized the application of equilibrium models for portraying the prominent features of the chemical composition of this system. His analysis, for example, has indicated that contrary to the traditional view, the pH of the ocean is not buffered primarily by the carbonate system his results suggest that heterogeneous-equilibria of silicate minerals comprise the principal pH buffer systems in oceanic waters. This approach and its expansion have provided a more quantitative basis for Forchbammer s suggestion of 100 years ago that the quantity of the different elements in sea water is not proportional to the quantity of elements which river water pours into the sea but is inversely proportional to the facility with which the elements in sea water are made insoluble by general chemical actions in the sea. 

Nenes A, Pandis SN, Pilinis C (1998) ISORROPIA a new thermodynamic equilibrium model for multiphase multicomponent inorganic aerosols. Aquat Geochem 4 123-152... 

Geist, A. 2008. Equilibrium model for the extraction of Am(III), Eu(III), and HN03 into DMDOHEMA in TPH. 2008. ATALANTE 2008 Nuclear Fuel Cycles for a Sustainable Future, May, Montpellier, France. 

General Equilibrium Model for Energy-Economics-Environment... 

Figure 7 further shows that, as gaseous C02 moves up the absorber, phase equilibrium is achieved at the vapor-liquid interface. C02 then diffuses through the liquid film while reacting with the amines before it reaches the bulk liquid. Each reaction is constrained by chemical equilibrium but does not necessarily reach chemical equilibrium, depending primarily on the residence time (or liquid film thickness and liquid holdup for the bulk liquid) and temperature. Certainly kinetic rate expressions and the kinetic parameters need to be established for the kinetics-controlled reactions. While concentration-based kinetic rate expressions are often reported in the literature, activity-based kinetic rate expressions should be used in order to guarantee model consistency with the chemical equilibrium model for the aqueous phase solution chemistry. 

The FREZCHEM model is a chemical equilibrium model. For a reaction such as gypsum dissolution... 

Yoshida, K., Shigeoka, T., Yamauchi, F. (1983b) Non-steady state equilibrium model for the preliminary prediction of the fate of chemicals in the environment. Ecotox. Environ. Safety 7, 179-190. 

By using the fundamental. principles of conservation of mass and charge, and chemical equilibrium expressions, the concentration of individual species in solution (sometimes called the "species distribution") can be calculated. The available equilibrium models for lime or limestone based FGD are the Bechtel-modified Radian equilibrium program (BMREP) (4) and the species distribution model (SDM)... 

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