Pure-fluid spinodal

Since this condition is also satisfied by the critical point, a pure-fluid critical point must lie on the spinodal. For a pure substance that obeys the Redlich-Kwong equation of state, the spinodal temperatures and volumes are related by... 

Along any pure-fluid, subcritical isotherm, the spinodal separates unstable states from metastable states. At the other end of an isotherm s metastable range, metastable states are separated from stable states by the points at which vapor-Uquid, phase-equilibrium criteria are satisfied. Those criteria were stated in 7.3.5 the two-phase situation must exhibit thermal equilibrium, mechanical equilibrium, and diffusional equilibrium. Since we are on an isotherm, the temperatures in the two phases must be the same, and the thermal equilibrium criterion is satisfied. 

These conditions identify both vapor-liquid and liquid-liquid critical points. For vapor-liquid equilibria, they are satisfied when the spinodal coincides with the vapor-liquid saturation curve. However, that point need not occur either at the maximum in the saturation envelope or at the maximum in the spinodal see Figure 8.12. Along a spinodal the one-phase metastable system is balanced on the brink of an instability at a critical point that balance coincides with a two-phase situation and the resulting fluctuations cause critical opalescence, just as they do at pure-fluid critical points. 

Figure 9.3 Along subcritical isotherms for pure fluids, the fugacity passes through stable, metastable, and unstable regions just as does the pressure. Here we have plotted the subcritical isotherm TlT = 0.863 for a van der Waals fluid. Each point (a-f) on the fugacity plot corresponds to the point of the same label on the Pv diagram. Points b and e have the same fugacity and pressure (P /= 0.539) and therefore locate the vapor-liquid equUibrium state. Points c and d are on the spinodal. Line segment be locates metastable liquid states segment de locates metastable vapor states segment cd locates unstable states.

The time evolution of phase separation by spinodal decomposition is described by a diffusion equation for the density (pure fluid) or species concentration (mixture) [101,103,105]. To illustrate the basic aspects of the theory, we consider the onedimensional, pure fluid case. Generalization to more dimensions, and extension to binary incompressible mixtures involve just a change of notation. For a pure fluid, the diffusion equation reads... 

Figures. Stability fields, calculated by the Anderko andPitzer equation of state of the HzO-NaCl system in a pressure-temperature diagram. Solid lines the saturation curve (LG) of pure water and the spinodal isopleths of p[fD-NaCl fluids (numbers refer to the mole fractions of NaCl). Dotted lines the liquid spinodal curve Sp(L, Hfd) and gas. spinodal curve Sp(G, HfJ) of pure water.

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