Equilibrium, Stability, and Criticality

Equilibrium, stability, and criticality arc important concepts that are closely related. In this chapter, after the formulation of simple methods for phase-equilibria calculations, the concepts of stability and criticality are introduced, and the application of the Gibbs free energy surface analysis to phase-equilibrium calculations is demonstrated. Then the stability and criticality concepts are presented in detail. These concepts are useful for a broad range of problems in engineering and physics. 

Suppose we are given a mixture of different species at a given temperature and pressure. If we know that the given mixture will split into two phases, say a gas phase and an oil phase, then we want to calculate the amount as well as the composition of each phase. This type of calculation is called the two-phase flash. In a more complicated case, we may not know into how many phases the mixture will split. Use of phase stability analysis provides a sound basis for such a situation. 

The stability concept is also useful in establishing the maximum supersaturation that can occur for both pure components and multicomponent mixtures. Suppose we are given a mixture of Ci and nC that has a fixed bubblepoint pressure at a given temperature. If the pressure of this mixture at the given temperature is lowered from a pressure above to a pressure below the bubblepoint, the gas phase may not appear if the pressure reduction is carried out rapidly. However, there is a theoretical limit for the pressure at which the gas phase will appear no matter how fast is the pressure reduction. This maximum supersaturation can be calculated from the stability limit to be discussed in this chapter. In the last part of this chapter, we will present methods that can be used in calculating the critical point of complex 

In this chapter, there is a strong emphasis on step by step derivations of the criteria of stability and criticality, mainly relying on the Second Law and its equivalent forms. We would like to comment that, to the best of our knowledge, the stability criteria and concepts have not yet been developed for multicomponent systems with curved interfaces. 

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