Simple Examples of Reactions with No Possible Multiple Steady States

1 Simple Examples of Reactions with No Possible Multiple Steady States 

We should realize that certain chemical/biochemical problems can have no multiplicities of their steady states over their entire range of parameters. Consider, for example, a simple first-order reaction process A = B with the rate equation 

Thus the reactant consumption function C(Ca) on the right-hand side of (3.23) is a straight line with slope a, or C Ca) = a Ca, and the reactant supply function S(Ca) on the left-hand side of (3.23) is S(Ca) = Cas — Ca- We can easily solve (3.23) graphically to find the steady-state solution Cass, since the steady state occurs when C(Cass) = S(Cass), or at the intersection of the two lines. 

Chapter 3 Some Models with Scalar Equations 

Note that for a nonisothermal CSTR we will always obtain unique solutions (no bifurcation) for endothermic reactions, defined by [3 0, for both the adiabatic and the nonadiabatic cases. 

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