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Transient behaviour of branched polymer melts through planar abrupt and rounded contractions using pom–pom models

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Abstract

In this paper, we study the transient flow of branched polymer melts with contrasting shear and elongational properties in planar 4:1 abrupt and rounded-corner contractions. This includes Single and Double Extended forms of the Pom–Pom model (SXPP and DXPP), comparing the transient behaviour for these two different models. With the DXPP version, the evolution of the molecular-chain backbone stretch (λ) is described by a dynamic equation, whilst in the SXPP form, stretch is an instantaneous algebraic function of the stress tensor (τ). Simulations are performed with a hybrid finite volume/element algorithm. The momentum and continuity equations are solved by a Taylor–Galerkin/pressure-correction finite element method, whilst the constitutive equation is dealt with by a cell-vertex finite volume algorithm. We demonstrate some novel features due to the influence and imposition of realistic transient boundary conditions on evolutionary flow-structure. The different effects of various model parameter choices are also exposed through transient field response in principle stress difference fringe patterns, rates of deformation, first and second normal stress difference, stress and stretch.

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Abbreviations

Symbol:

Name

U :

fluid velocity

p :

hydrodynamic pressure

τ :

extra-stress

t:

time

d :

rate of deformation tensor

I :

unit tensor

\(\mathop{\boldsymbol{\tau}} \limits^{\nabla}\) :

upper-convected material derivative of τ

Re :

Reynolds number

We :

Weissenberg number

U :

characteristic velocity

L 0 :

characteristic length

ρ :

fluid density

μ :

fluid viscosity

μ p :

Polymeric component

μ s :

Newtonian solvent component

β :

solvent fraction ratio

q :

number of side-branch arms

ε :

system entanglement

λ :

stretch of back-bone segment

α :

anisotropy parameter

λ 0b :

backbone-orientation relaxation time

λ 0s :

backbone-stretch relaxation time

G 0 :

linear relaxation modulus

N 1 :

first normal stress difference

N 2 :

second normal stress difference

\(\dot{\gamma}\) :

shear-rate

\(\dot{\varepsilon}\) :

extension-rate

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Authors and Affiliations

  1. Institute of Non-Newtonian Fluid Mechanics, College of Engineering, Swansea University, Swansea, SA28PP, UK

    H. R. Tamaddon Jahromi & M. F. Webster

Authors
  1. H. R. Tamaddon Jahromi
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  2. M. F. Webster
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Correspondence to M. F. Webster.

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Tamaddon Jahromi, H.R., Webster, M.F. Transient behaviour of branched polymer melts through planar abrupt and rounded contractions using pom–pom models. Mech Time-Depend Mater 15, 181–211 (2011). https://doi.org/10.1007/s11043-010-9130-9

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  • DOI: https://doi.org/10.1007/s11043-010-9130-9

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