Flow diagram and stationary states

In the spirit of plotting the rates of reaction and net inflow against extent of conversion, Figs 6.7(a) and (b) show R and L as functions of the extent of conversion, 1 — a, from eqn (6.20) for a typical non-zero value of / 0. 

The reaction rate curve R is zero at complete conversion and also has low (but non-zero) values close to 1 — a = 0, with a maximum close to two-thirds conversion (actually at 1 — a = — / 0). Importantly, R does not depend on the residence time rres, although it does vary if / 0 is changed. The flow line L is zero when 1 — a = 0 since the inflow and outflow have the same composition (no conversion of A to B). The gradient of the flow line (Fig. 6.7(b)) is given by 1 /Tres, so it is steep for short residence times (fast flow rates) and relatively flat for long rres. (Note how tres actually compares fres and lch, so short residence times are those that are much less than the chemical timescale etc.) The flow line is, however, unaffected by the inflow concentration of the autocatalyst f 0. 

The full 1 — ass versus rres bifurcation diagram is shown in Fig. 6.7(e) and reveals an S-shaped curve. Between the two turning points is a region of 

Influence of autocatalyst inflow on multiple stationary states 

L should be equal and they should have equal slope, i.e. we require simultaneously that 

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FLOW DIAGRAMS AND STATIONARY-STATES (ILLUSTRATED FOR SYSTEMS WITH A STABLE CATALYST)... 

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