| A 3-D numerical simulation model was proposed to predict the polymerization of epsilon-caprolactone in fully-filled conveying elements and kneading blocks of co-rotating twin-screw extruders, in which the kinetics equation for polymerization is coupled with continuity equation, momentum equation, and energy equation. With the 3-D model, parametric studies have been carried out to investigate the effects of screw configurations, screw diameter, operational conditions, values of heat from reaction, initiator concentration, and heat transfer conditions at barrel surface upon the polymerization progress. Two simulation models for the polymerization in the partially-filled channels were developed based on the conveying mechanisms of the reaction system in the screw channels. Finally, a global model for reactive extrusion was proposed, combining the models for the fully-filled screw elements and the partially-filled channels.;The predicted conversion ratios at the die based on the 3-D model agree well with the experimental results from the literature, indicating that the proposed 3-D model for polymerization in twin-screw extruders is reliable. Three indexes, i.e. flux-mixing coefficient, temperature mixing coefficient, and conversion ratio mixing coefficient, are defined for the first time to evaluate the axial mixing during reactive extrusion. Moreover, transverse mixing is characterized with the ratio of pressure flow rate to net flow rate in axial cross sections.;The simulation results based on the 3-D model indicate that the polymerization of epsilon-caprolactone in screw elements depends not only on the mixing mechanism and flow behavior, but also on the heat generation in the reaction system and the heat transfer at the barrel surfaces. It is proposed that the optimization of polymerization in twin-screw extruders can be achieved by matching the flow and mixing mechanisms with the energy generation and energy loss. The application of 1-D model, a commonly used method in the simulation of reactive extrusion, in predicting the polymerization progress in reactive extrusion is acceptable only under certain conditions, such as a small screw diameter, a short fully-filled length, a low screw rotating speed, and a small heat from reaction.;The investigation in scaling up polymerization in twin-screw extruders with the 3-D model reveals that the polymerization is completed in shorter screw length (in unit of screw diameter) with increasing screw diameter, due to the non-uniformity in temperature in large extruders. The optimizations of screw configurations, operational conditions, and cooling systems are extremely important to the polymerization in large machines, in which 3-D model is a valuable tool. |
