An Analytical Non-Newtonian and Nonisothermal Viscous Flow Simulation

Abstract

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.

The finite element analysis of melt flow behaviour in micro-injection moulding

“…For a Newtonian model the viscosity is independent of the shear rate [10]. Polymer melts are not Newtonian and the viscosity is a function of t and g. Therefore, a typical plot of t against g of such flows has complex velocity profiles.…”

Rheological Investigation of Hydroxypropyl Cellulose–Based Filaments for Material Extrusion 3D Printing

“…The rheological properties of the polymer melt play an essential role in determining the optimal conditions of the extrusion and the properties of the extruded object. The extrudability/printability of filaments and the reproducibility of the extruded/printed structures depend on the polymer’s response to extrusion, the polymer’s ability to adhere to previously printed layers and the firmness of the weight of the subsequent layers [ 10 ], which were controlled by the material flow [ 40 ], temperature of the melt through viscous dissipation [ 40 , 41 ] and shear rate [ 40 , 42 ]. Previous research has studied the relationship of temperature and the structural morphology [ 43 , 44 ], and the effect of bonding formation coupled with microstructure observation, using multiscale damage analysis [ 45 ].…”

An iterative stabilized CNBS–CG scheme for incompressible non-isothermal non-Newtonian fluid flow

“…The numerical simulation of non-Newtonian fluid flow has attracted increasing attentions due to its comprehensive applications to engineering practices such as chemical process industries, food and construction engineering, petroleum production, bioengineering, etc [9][10][11][12][13][14]. As compared with the numerical solution procedure for the Newtonian fluid flow governed by incompressible N-S equations, non-linearity of the solution procedure for the non-Newtonian fluid flow stems from not only the convective term in the momentum equation but also the variation of its viscosity with respect to strain rates depending on distributions of the primary variables, i.e.…”