Simulating Polymer Mixing Processes Using the Boundary Element Method

Abstract

Abstract The mixing of plastic into filled and unfilled polymer blends has been an important issue in the polymer industry. Processing difficulties with these polymers have been encountered in the mixing quality as well as in the thermal degradation due to viscous heating. Mixing often occurs as an element of the processing step, e.g., inside single and twin screw extruders used in the fabrication of final parts or sheets, and inside internal mixers such as the Banbury type mixer. Quantifying the mixing inside an extruder or an internal mixer and predicting the thermal degradation due to viscous heating is an extremely difficult task. A better understanding of the mixing process and control of viscous heating will lead to optimal parts and may eventually allow us to increase the relative amount of fillers within the material. This paper presents a boundary element simulation of the flow of filled and unfilled polymer blends inside extruders and internal mixers. First, the general equations that govern such flows are shown. The boundary integral equation and the fundamental solutions are then formulated followed by the numerical implementation and logistics of the simulation. After the theoretical background is presented, a numerical example is given. The paper then shows how the simulation was used to analyze the flow inside a single screw extruder and internal batch mixers. Such a simulation can be used to eliminate some of the tedious trial-and-error tasks that are typically performed in the early stages of material synthesis and can also be used by manufacturers of mixing equipment when optimizing the geometries of cavities and mixing heads to achieve optimum mixing with reduced viscous heating. This research will significantly increase our knowledge of the behavior of filled and unfilled polymer blends and expand our understanding of the complex phenomena that take place during their mixing process.