| The modelling, simulation, and stability of emulsion polymerization in a continuous stirred-tank reactor are considered in this study. The mathematical model is derived from a polymer particle population balance and includes such mechanistic detail as: particle formation via micellar initiation, coupling of the aqueous and particle phase free radical concentrations, thermodynamic equilibrium between the aqueous and particle monomer phases, and the gel effects for propagation, chain transfer, and termination reactions.; The model is solved efficiently using orthogonal collocation on finite elements. Dynamic and steady-state simulations are compared to experimental measurements of conversion, total particle number, and particle size distribution for styrene, methylmethacrylate, and vinyl acetate polymerizations. Reasonably good agreement between the simulations and experiments is achieved without parameter adjustment.; The model is capable of predicting all of the experimentally observed phenomena including steady-state multiplicity, sustained oscillations, ignition and extinction dynamics, and overshoot in conversion during start up. In addition, a new multiplicity due to radical desorption has been predicted that has not yet been observed experimentally.; The stability of the reactor is determined using both comprehensive and simplified models. The simple model shows that Smith-Ewart case II kinetics cannot predict oscillations for any values of the operating parameters. Kinetics based on an approximation to the general Stockmayer-O'toole relation do predict oscillations. An analytic criterion determining the stability of the steady state is given for this case.; Numerical techniques are developed to determine the bifurcation structure of the comprehensive model, which consists of coupled partial differential, differential, and algebraic equations. The methodology is illustrated by showing the branching to limit cycles and multiple steady states for the methylmethacrylate system. The radical desorption rate and reactor residence time have the strongest influence on the existence of the limit cycles. |
