On flows of viscoelastic liquids in long channels and dies

General non-existence of steady rectilinear viscoelastic flows in long tube s results in occurring secondary flows. The early analytical and experiment al studies of dilute polymer solutions as well as recent experiments and di rect numerical simulations of polymer melts found the secondary flows to be very weak. It suggests that for many applications to polymer processing th e secondary flows can either be neglected or when necessary, treated as sma ll disturbances relative to rectilinear flow component. The paper develops and justifies an approach based on partitioning flow in the main, quasi-rec tilinear part and small disturbances, The formulated quasi-rectilinear flow problem is described by a second order non-linear elliptic PDE that is clo se to simple shearing. The calculations of main axial velocity profiles emp loying this approach are successfully compared with recent experimental dat a. Using a perturbance procedure a forth order linear PDE for secondary flo ws is then derived, In contrast to the quasi-rectilinear flows whose descri ption needs only knowledge of three shear viscometric functions, computatio ns of secondary flows depend on features of viscoelastic constitutive equat ions. Scaling evaluations and calculations of two secondary flow problems f or simple geometry confirm that these flows are very weak. (C) 2001 Elsevie r Science Ltd. All rights reserved.