An Analytical Non-Newtonian and Nonisothermal Viscous Flow Simulation

Polymer process control is limited by a lack of observability of the distributed and transient polymer states. An analytical solution is presented for on-line simulation of non-Newtonian and nonisothermal viscous flow in real-time polymer processing. The modeling of the non-Newtonian viscous flow utilizes a modified Ellis model that expresses viscosity as a function of shear stress; the modeling of the heat transfer utilizes a Bessel series expansion to include effects of heat conduction, heat convection, and internal shear heating. The resulting simulation is suitable for inclusion in real-time process controllers requiring sub millisecond response. Numerical verification indicates that the flow rate predictions of the described analysis compare well with the results from a commercial molding simulation. However, empirical validation utilizing a design of experiments for an injection molding process indicates that the described analysis is qualitatively useful but does not possess sufficient accuracy for quantitative process and quality control.