Regions of stability and instability

The division of the parameter plane into regions of stability and instability is reproduced in Fig. 10.3. If pi and k lie within the closed region, the stationary state is unstable and spatially uniform oscillations exist. 

The MASC (for "multicomponent adsorption simulation calculations") computer program, which identifies the regions of stability and instability within the sorption fronts, the distance which the front must travel through the bed for the potentially stable regions to attain their ultimate steady-state... 

Figure 6.7. Region of stability and instability as determined by p AB, based on first-order deviation from SI solutions.

In section 6.6, we have examined the conditions for stability using the first-order deviations from SI solutions. The regions of stability and instability were summarized in figure 6.7. 

Much work has been done on the regions of stability and instability using empirical expression for the excess free energy see, for example, Prausnitz et al. (1968) and Novak et al. (1987). 

Figure 6.8. Region of stability and instability based on the exact KB expression (6.127).

Finally, we note first that in all our calculations, we have assumed that pAAB is constant in the entire range of composition. In real systems we should expect that pAAB will change with composition. This will affect the details of the regions of stability and instability but grossly the qualitative behavior should not be much different. In figure 6.12, we present two examples of the behavior of the second derivative of g for two cases when pAAB depends linearly on xA. Second, we recall that the KB theory and the... 

Figure 5. Schematic representation of stability and instability regions.

Fig. 8. The stability and instability regions of a polystyrene latex with added aluminum salt at different pH values (17).

The location and shape of the distribution curve is, of course, dependent on which branch of the hysteresis loop is used to compute the pore size. In spite of the considerable attention given to this problem, in the absence of any detailed knowledge of the pore geometry it is not possible to provide unequivocal general recommendations. In principle, the regions of meta-stability and instability should be established for the liquid/vapour meniscus in the various parts of a given pore structure, but in practice this would be extremely difficult to undertake in any but the simplest types of pore system. 

Fig. 43 and 44. Curves separating regions of stability from regions of instability, the curves uniting points where the stability ratio W Monovalent electrolyte. 

Fig. 10 and prove that in the case of three steady states Xj, < X2 < X X2 is instable whereas X and are locally and asymptotically stable. What are the local stability regions of X and X ... 

Eq.uation (lO) represents the binary spinode and serves to delimit regions of thermodynamic stability and instability with respect to compositional unmixing. 

Figure 4.3. 1 Phase diagram of a macromolecular solution whose phase separation occurs through a decrease of temperature (UCST). 2 Variation of the average free energy of mixing as a function of the voiume fraction of the soiute (a) formation of a homogeneous solution at T2 (b) demixing in two phases for compositions between p and p" at 7. S, M, I indicate the regions of stability, metastability, and instability, respectively.

FIGURE 9.27 Stability and instability regions in the space Wf and Sr, for X = 16. (Reprinted by permission of the publisher from Kanai and White, 1984.)... 

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