Melt flow of biopolymer through the cavities of an extruder die: Mathematical modelling

This is an analytical solution of the two-dimensional non-isothermal mathematical model describing the change in the velocity profile of a cylindrical extrusion die. This solution is based on the following assumptions. The two-dimensional melt flow is asymmetric. A melt viscosity anomaly may take place. Heat generated by viscous friction is a factor affecting the melt flow. The melt flow moving towards the metering section is in a steady state. Neither mass forces nor inertia forces are present. Velocity gradients along the channel are neglected. The mathematical model was built up from the incompressibility equation, motion equations, energy equation, and the rheological equation. This model depicted a non-isothermal flow of rheological fluid moving through the cylindrical extrusion die. A diagram was drawn. It depicts the melt velocities at a die entrance in different cross-sectional views. Computer testing was performed to verify the obtained solutions and compare them with the real extrusion process. Difference between calculated and experimental data was below 14%. Results allow concluding a matching of numerical results with experimental data, and so the possibility of using a built-up model in an extrusion die design for single-screw extruders.