callen_solution_thermodynamic_9pn1a v1.0.0

Callen Solution Thermodynamic

Callen Solution Thermodynamic ->->->-> https://blltly.com/2thSBj

The authors obtain a new form of the modified Kohler Equation (7) which leads to a system of equations that incorporates any number of liquid-liquid phase equilibria. The derivation is based on an expansion of the thermodynamic potential function around any point that is near the most stable solution. The resulting modified Kohler equation is identical to the traditional KB equation, except that the surface tension terms are dependent on the near solution state. Surface tension coefficients for several solutions are tabulated, and the equations are applied to several vapor-liquid equilibrium problems including the liquid-liquid equilibria of a binary mixture (sulfuric acid and phosphoric acid) and a ternary (ammonia-water-nitric acid) mixture. The calculated data are in good agreement with experimental data for all of the systems tested. Finally, the authors extend the theory to include an additional term in the modified Kohler Equation, which leads to approximation of the thermodynamic potential to higher order.

The authors have extended the theory developed in Orkand’s 1993 paper 1 to include both the kinetic and kinetic/thermodynamic terms for single component droplet-vapor and multiple component gas-liquid phase equilibria. They have also extended the theory for equilibrium limited crystallization. The modified Kohler theory has been applied to solidification and crystallization of water and benzene from superheated vapor. The theoretical results compare favorably with experimental data from drops of either superheated water or superheated benzene.

This is a critical review of the mathematical derivation and thermodynamic treatment of the Modified Kohler Equation (MKE) as given in Orkand and Rabold’s 1993 paper 1 and to the extension of this theory to multiple component single phase and two component multiple phase phase equilibria including solidification and crystallization. Calam and Melson’s 1991 paper 2 also provides a strong mathematical motivation and thermodynamic rationale for this theory. The modified theory is presented in a way which allows a separate derivation of each of the components in the systems. The modified theory leads to the original Kohler theory when the fluid is highly dilute. Alternatively, in the high concentration limit, the modified theory reduces to the conventional gradient theory except that the surface tension coefficients are dependent on the local solution state. The most important result is the introduction of an additional volume-dependent surface tension coefficient. The authors show that this coefficient leads to a surface reaction rate which is relevant for droplet-vapor equilibria and provides the correct behavior for concavity and convexity with respect to the solute concentration in a two component vapor-liquid system. Finally, the theory is extended to treat vapor-liquid equilibria in binary and ternary mixtures. In the case of binary mixtures of a single component and a two component vapor-liquid mixture, the thermodynamic representation is based on only two matrices, instead of three, and simplifies calculations. In ternary mixtures, the authors introduce a matrix, called G~2, and show that it can be used to represent a system with three non-binary components. This theory is shown to lead to the same surface tension coefficients as the two component case, except for the chemical potential terms. 84d34552a1