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Modeling spurt and stress oscillations in flows of molten polymers

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Abstract

The paper presents an approach for modeling polymer flows with non-slip, slip and changing non-slip — slip boundary conditions at the wall. The model consists of a viscoelastic constitutive equation for polymer flows in the bulk, prediction of the transition from non-slip to sliding boundary conditions, a wall slip model, and a model for the compressibility effects in capillary polymer flows. The bulk viscoelastic constitutive equation contains a hardening parameter which is solely determined by the polymer molecular characteristics. It delimits the conditions for the onset of solid, rubber-like behavior. The non-monotone wall slip model introduced for polymer melts, modifies a slip model derived from a simple stochastic model of interface molecular dynamics for cross-linked elastomers. The predictions for the onset of spurt, as well as the numerical simulations of hysteresis, spurt, and stress oscillations are demonstrated. They are also compared with available data for a high molecular weight, narrow distributed polyisoprene. By using this model beyond the critical conditions, many of the qualitative features of the spurt and oscillations observed in capillary and Couette flows of molten polymers, are described.

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Abbreviations

\(\mathop {\underline{\underline c} }\limits^\triangledown\) :

upper convected derivative of elastic strain tensor \(\underline{\underline c}\)

f, fm, fmin :

dimensionless (sliding) shear friction characteristics, and its maximum and minimum

G:

Hookean elastic modulus

Gp :

plateau modulus

G′, G″:

storage and loss moduli

I1, I2 :

first and second invariant of strain tensor \(\underline{\underline c}\)

I1, I0 :

capillary and barrel lengths

M:

non-dimensional mass flow rate

MC :

critical molecular weight

M*, Me :

molecular weights of a statistical segment, and of polymer chain between entanglements

Mn, MW :

number average and weight average molecular weights

m, k :

two fitting parameters of slip model

ν s , ν os :

nominal and characteristic sliding velocities

u :

non-dimensional sliding velocity

u sc :

initial (infinitesimal) slip velocity

u 1 :

upper limit of u on the lower branch

u 2 :

lower limit of u on the upper branch

u max :

value of u corresponding to fmin

u min :

value of u corresponding to fmax

U:

piston speed

Q:

nominal volumetric flow rate

q:

non-dimensional volumetric flow rate

R, Ro :

capillary and barrel radii

M:

non-dimensional mass flow rate

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  1. Department of Polymer Engineering, University of Akron, 44325-0301, Akron, Ohio, USA

    Kolapo P. Adewale &  Arkady I. Leonov

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Adewale, K.P., Leonov, A.I. Modeling spurt and stress oscillations in flows of molten polymers. Rheola Acta 36, 110–127 (1997). https://doi.org/10.1007/BF00366817

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