Determination of polymeric medium flow rate in extruders based on a new correlation

Abstract

One of the most widespread practical methods of polymer processing is the extrusion method that is based on pressing a polymeric melt through channels of the molding tool which have different geometrical crosssections. The basic performance of extrusion is based on the pressure and flow performance which sets functional correlation between volumetric flow rate of a polymer medium, pressed through a molding tool, and created pressure drop. Arguments of this correlation are the rheological parameters of polymer and the geometrical characteristics of the channel in which the polymeric melt flows. In this article, a viscoelastic model with a corrected strain energy function is implemented. The comparison of revealed theoretical expression in this article with the experimental data for flow of polymeric melts in cylindrical channels with various cross-sections demonstrates a good convergence over a wide range of pressure gradient. POLYM.

Flow/pressure characteristics and modeling of deformation processes of single‐screw extruders

“…For consideration both viscous and elastic properties of polymeric melts, following viscoelastic model is implemented [5, 14]. where $\overline \sigma$ denotes (::) stress tensor; P , Lagrange multiplier, determined by boundary condition; $\overline \delta$ , identity tensor; $\overline c$ , Cauchy strain tensor; ${\overline e}_{\rm {f}}$ , flow strain rate tensor; $\overline \omega$ , vortex tensor; $\overline e$ , strain rate tensor; θ 0 ( T ), relaxation time; G 0 ( T ), tensile modulus; W , strain energy function W = W ( I 1 , I 2 ); I 1 and I 2 , primary and secondary strain tensor invariants; ψ, dimensionless parameter $(\psi = 0\;{\rm{at}}\;\overline \omega = 0\;{\rm{and} }\psi = I\;{\rm{at}}\;\overline \omega \ne 0)$ ; f ( I 1 , I 2 ), dimensionless function that defines relaxation time, and $2W^{\rm S} = W(I_1, I_2 ) + W(I_2, I_1 )$ , symmetric function of W .…”

“…Most researchers use Mooney‐Rivlin potential, but there are differences between experimental and theoretical results for prediction of stress and strain. Results of recent research show that in various kinematical deformations, the following potential can be used [5]. …”

“…where A 1 , B 1 are constants of integration. For consideration both viscous and elastic properties of polymeric melts, following viscoelastic model is implemented [5,14].…”

“…The interplay between extruder configuration, operating conditions, and polymer rheology is important in dictating the final properties of the extrudate. The rheological properties of the polymer have a significant impact on fluid flow in an extruder [1][2][3][4][5].…”