Critical state instability limit

No theoretical criterion for flammability limits is obtained from the steady-state equation of the combustion wave. On the basis of a model of the thermally propagating combustion wave it is shown that the limit is due to instability of the wave toward perturbation of the temperature profile. Such perturbation causes a transient increase of the volume of the medium reacting per unit wave area and decrease of the temperature levels throughout the wave. If the gain in over-all reaction rate due to this increase in volume exceeds the decrease in over-all reaction rate due to temperature decrease, the wave is stable otherwise, it degenerates to a temperature wave. Above some critical dilution of the mixture, the latter condition is always fulfilled. It is concluded that the existence of excess enthalpy in the wave is a prerequisite of all aspects of combustion wave propagation. 

It follows that the evaluation of the extent to which one-dimensional physics is relevant has always played an important part in the debate surrounding the theoretical description of the normal state of these materials. One point of view expressed is that the amplitude of in the b direction is large enough for a FL component to develop in the ab plane, thereby governing most properties of the normal phase attainable below say room temperature. In this scenario, the anisotropic Fermi liquid then constitutes the basic electronic state from which various instabilities of the metallic state, like spin-density-wave, superconductivity, etc., arise [29]. Following the example of the BCS theory of superconductivity in conventional superconductors, it is the critical domain of the transition that ultimately limits the validity of the Fermi liquid picture in the low temperature domain. 

We have shown how models for volumetric equations of state can be used with stability criteria to predict vapor-liquid phase separations. However, not all phase equilibria are conveniently described by volumetric equations of state for example, liquid-liquid, solid-solid, and solid-fluid equilibria are usually correlated using models for the excess Gibbs energy g. When solid phases are present, one motivation for not using a PvT equation is to avoid the introduction of spurious fluid-solid critical points, as discussed in 8.2.5. A second motivation is that properties of liquids and solids are little affected by moderate changes in pressure, so PvT equations can be unnecessarily complicated when applied to condensed phases. In contrast, g -models often do not contain pressure or density instead, they attempt to account only for the effects of temperature and composition. Such models are thereby limited to descriptions of phase separations that are driven by diffusional instabilities, and the stability behavior must be of class I (see 8.4.2). In this section we show how a g -model can describe liquid-liquid and solid-solid equilibria. 

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