Nature of Pinch Points

The preceding section shows that there are in fact many types of nodes to consider, each with their own mathematical description. It is, however, useful to have an understanding of when one may expect a certain stationary to be of a certain nature. 

TABLE 3.1 Three DifTerent Cases of Pinch Point Solutions for a Constant Relative Volatility Ternary System 

Case Number Nature of Solutions Type of Nodes Real Roots 

2 X =[Ri,K2,M3] with IR2 = 1 3 Asymptotically stable/unstable node + half unstable saddle/half stable saddle node 2 

Furthermore, due to the fact that negative compositions are permissible, we have to account for all types of steady-state solutions to the DPE, including complex solutioas. In fact, complex solutions are not that rare in CPMs, and CSs displaying these properties are perfectly normal. For a constant relative volatility ternary system which only has three roots, there are three unique cases that may occur, as summarized in Table 3.1. 

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