Helical flow of a viscoelastic fluid−An approximation towards the analysis of rotational extrusion

Helical flow of a polymer melt is analyzed using nonlinear viscoelastic constitutive theory with and without inclusion of the shear stress components, τ₁₃, arising due to an interaction of two shear flows. The problem of helical flow is approximated by considering flow between two parallel plates with one plate moving at constant velocity orthogonally to the main pressure‐driven flow. The governing equations involved in the theory are derived and then solved along with the equation of motion using numerical techniques. The gapwise distributions of shear rates, shear and normal stresses, viscosity, and velocities are obtained, as well as torque and pressure‐throughput relationships. The predicted data for pressure‐throughput relationships are compared to results obtained from rotational extrusion experiments carried out for polystyrene and polypropylene melts exhibiting, respectively, high and low sensitivity of viscosity to temperature. The isothermal solution with or without inclusion of τ₁₃ was found to be unable to quantitatively predict pressure drops for helical flow especially at low flow rates and high rotational velocities. For the case of τ₁₃=0, a simplified approach to nonisothermal flow, based on adiabatic temperature rise due to viscous heating, is presented. The nonisothermal approach with τ₁₃=0 is found to correctly describe experimental pressure‐flow rate data for both polymers. The inability of the theory with τ₁₃≠0 to describe the experimental data was possibly due to a significant overprediction by the theory of the second difference of the normal stresses.