Metastable states fluid mixture

However, the full instability criteria (8.5.1)-(8.5.3) still cannot distinguish stable states from metastable states but then, no differential test can make this distinction. To distinguish stable states from metastable states, we must apply an appropriate equilibrium criteria. For example, if T and P have been specified for a proposed state, then the stable state is the one that minimizes the Gibbs energy. Using this as a basis, we showed how to identify the stable state for pure fluids and for binary mixtures. 

As the size of the metastable region and the number of relaxation times by all the signs increase, the use of quasi-static methods becomes unacceptable. It is probably for this reason in part that research into not fully stable states of complex systems (mixtures and thermally unstable fluids ) progresses very slowly. To solve the problem, we are developing the method of controlled pulse heating of a thin wire probe - resistance thermometer. 

In Figure 8.12 the outer envelope is the locus of saturated equimolar liquid states and saturated equimolar vapor states. However, note that Figure 8.12 is not a phase-equilibrium diagram in Figure 8.12 every point on the two-phase line represents an equimolar mixture, but phases in vapor-liquid equilibrium generally do not have the same composition. Consequently, Figure 8.12 contains no tie lines across the two-phase region. Outside the saturation envelope, the mixtures are stable one-phase fluids. Underneath that envelope, the mixtures may be metastable one-phase fluids or they may be unstable to one phase (that is, they may exist as two-phases). 

The differential stability criteria were derived by finding conditions that maximize the total entropy in an isolated system. Those conditions constrain how the system responds to thermal, mechanical, and diffusional fluctuations. In the derivations, those constraints are conveniently posed as stability criteria they show us that a stable substance must always obey the thermal criterion (8.1.23), the mechanical criterion (8.1.31), and the diffusional criterion (8.3.14). But the converses of those statements are not always true for example, a mechanically stable fluid always has Kj > 0, but a fluid having Kj > 0 is not necessarily stable— it might be metastable. Therefore, in using these differential criteria (as opposed to merely deriving them), many ambiguities can be avoided if we repose each constraint in the form of an instability criterion such criteria identify those thermodynamic states at which a pure substance or mixture is differentially unstable. 

Note that for the small size ratios, for which the FVT of asymmetrie hard sphere mixtures is applicable, fluid-fluid demixing (also predieted by FVT, not shown) is metastable with respect to the fluid-solid transition. The presence of this metastable transition does affeet the physieal properties of the mixtures. Like colloid + polymer mixtures [11-13], asymmetrie hard sphere mixtures display interesting gel and glass states that are supposed to be eonneeted with the metastable fluid-fluid transition [14, 15],... 

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