Separatrixes saddle stationary point

The boundaries separating one bundle from another are specific residue curves that are called the separatrixes of saddle stationary points. In contrast to the other residue curves, the separatrixes begin or come to an end, not in the node points but in the saddle points. A characteristic feature of a separatrix is that in any vicinity of its every point, no matter how small it is, there are points belonging to two different bundles of residue curves. The concentration space for ideal mixtures is filled with one bundle of residue curves. Various types of azeotropic mixtures differ from each other by a set of stationary points of various types and by the various sequence of boihng temperatures in the stationary points. 

Figure 6.5 shows stationary points Sm and iV+ of trajectory bundles of intermediate section Reg j and separatrixes of saddle stationary point Sm obtained by means of calculation for ideal mixture pentane(l)-hexane(2)-heptane(3) at the composition of pseudoproduct x), = -1.0 x)) 2 = 1-5 3 = 0.5 and at the value... 

In contrast to nonsharp separation in the top and bottom sections, the intermediate section has at reversible distillation trajectory not just one node stationary point, but there are saddle point Sm and node point Nm- Separatrixes of the saddle points Sm divide concentration triangle into four regions Reg t trajectory bundles of intermediate section, one of which is the working one Reg jj,t-... 

At Ty es " 312.5, a saddle point and a stable node appear in the phase-plane, corresponding to the two other stationary-states. Shortly after this, the limit cycle grows sufficiently large to touch the separatrix of the saddle point and form a homoclinic orbit. The period of motion around this cycle becomes infinite and beyond this point oscillations are not found. There is thus a sudden quenching of large amplitude oscillations. For all residence times greater than = 313 the system sits at the lowest, stable state. There is also hysteresis at this limit. 

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