Tangency conditions for flow diagrams

This correspondence between tangency and jump points is quite universal in chemical models and so it is instructive to work the present simple case in 

In terms of the rate constants etc. for the present model, this becomes 

The upper root gives the tangency at low extents of conversion shown in Fig. 1.12(d), the lower root gives Fig. 1.12(b). The corresponding flow rates can then be evaluated by substitution from eqn(1.53) to (1.51). 

A response showing multiple stationary states requires that the inflow concentration of B be significantly less than that of A. Multiple intersections and tangencies are only possible if 

For larger inflow concentrations of the autocatalyst B, i.e. with b0 a0/8, the curves R and L can only intersect once, whatever the flow rate. As shown in Fig. 1.13, we then have a monotonic dependence of ass on kf. 

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