Degree Name

Doctor of Philosophy


School of Mathematics and Applied Statistics


Many process in chemical engineering occur in a flow reactor. When this reactor is well-mixed then the chemical process occurring within it are modeled by a system of ordinary differential equations. By ‘well-mixed’, it is meant that the concentration of a chemical at any point within the reactor is identical to that at any other point within the reactor. This is usually a good expectation for a small reactor, but it does not always hold true for industrial reactors where the reactor may be very large.

In this thesis I investigate how incomplete, or poor, mixing effects the performance of a number of chemical and biochemical processes. To model the effects of incomplete mixing a segregated reactor model is used in which the reactor volume is split into two compartments: one component represents a highly agitated region whereas the other component represents a stagnant region. The number of equations for the incomplete mixing model is twice that for the ideal bioreactor model. The incomplete mixing model has two parameters. The first represents the relative volume of the stagnant region to the total volume and the second represents the degree of mixing between the two regions.

Although this model was originally proposed over 40 years ago, it has not been investigated in detail. I apply it to a variety of chemical mechanisms in the fields of bioreactor engineering and non-linear chemical dynamics. The former are the Monod model and a model for a membrane-coupled anaerobic fermentor. The latter are the Belousov-Zhabotinskii reaction and a model for quadratic autocatalysis with a non-linear decay term.

The main technique used for both the ‘perfect mixing’ and ‘imperfect mixing’ reactor models is to find the steady-state solutions and determine their stability as a function of the residence time, which is the main experimental control parameter.

We find that the effect of incomplete mixing can not be to remove a transcritical bifurcation at which a washout branch loses stability. However it does change the value of the residence time at which the transition occurs. For other bifurcation the effect of incomplete mixing may be more significant. Both static and dynamic bifurcations can be eliminated by poor mixing.