Low-dimensional models for describing mixing effects in reactive extrusion of polypropylene

Abstract

Spatially averaged low-dimensional models based on Liapunov–Schmidt technique of bifurcation theory have been developed to study mixing effects in peroxide-induced reactive extrusion of polypropylene degradation. The two-dimensional convection–diffusion-reaction equations for each species and the energy balance equation have been averaged in the transverse direction to obtain low-dimensional models that describe transverse (local) mixing effects on conversion, average molecular weight and temperature distribution in a reactive extruder channel with asymmetric thermal boundaries. Our models predict that incomplete local mixing due to velocity distribution, backflow and transverse diffusion may significantly reduce the conversion (by more than 50%) in a reactive extruder, compared to a plug-flow case. Our analysis further reveals that beyond a transition value of Damköhler number ( Da), the overall reaction occurs in the mixing-limited regime, where the conversion and the average molecular weight of the polymer melt are determined only by the dimensionless local mixing time (which, in turn, depends on the screw speed) and are independent of Da. Increased Graetz number (i.e. slow transverse thermal diffusion) decreases the polymer-melt temperature and reduces conversion, while increase in screw speed increases viscous heat generation resulting in higher exit temperature accompanied by reduced conversion and produces off grade high molecular weight (low melt flow index) product when the mixing effect dominates the temperature effect.