## Abstract

Most commercially available computational fluid dynamics (CFD) simulation packages do not take into account the viscoelastic nature of polymers. Instead, generalized Newtonian fluid (GNF) flow models are used to describe the relation between the stress and rate of deformation tensors in order to solve the conservation equations of mass, momentum and energy. However, these models fail to predict empirically proven flow phenomena such as extrudate (die) swell and underestimate pressure drops in contraction flow areas.

The present study tests the applicability of the viscoelastic Kaye-Bernstein–Kearsley–Zapas (K-BKZ) rheological model to both a pure gum acrylonitrile–butadiene rubber (NBR) as well as a carbon black filled NBR compound. This integral constitutive equation is based on a time- and deformation-dependend polymer network.

First, small amplitude oscillatory shear (SAOS) tests are carried out for the characterization of storage and loss moduli. Second, time-temperature superposition (TTS) is performed to extend the accessible frequency range at the reference temperature. Finally, the steady-state shear and apparent extensional viscosity is calculated from high pressure capillary rheometry (HPCR) data. These rheological properties are subsequently used to fit the viscoelastic K-BKZ (Wagner), the viscoplastic Herschel-Bulkley and the viscous power-law models.

Next, two-dimensional axisymmetric finite element models of three abrubt capillaries and one tapered orifice die are built in the commercial software package ANSYS Polyflow aiming to predict measured pressure drops of the HPCR experiment.

For the unfilled gum NBR the K-BKZ (Wagner) simulation results match experimental data almost perfectly. As expected, the viscous power-law model underestimates pressure drops with an avarage deviation exceeding 38 %.

Adding fillers to a polymer matrix increases the linear viscoelastic moduli but decreases entropy elastic flow phenomena. This behavior is pronounced at high filler loadings (occluded, trapped rubber) especially when adding active particles like carbon black (bound rubber). However, the K-BKZ (Wagner) model is not able to reflect this relation in its current mathematical formulation. To ensure its applicability to highly filled polymer systems: (1) a dependency on the effective filler volume and (2) a (visco)plastic term must be added. This task will be addressed by the groups of Walter Friesenbichler, Evan Mitsoulis, Ines Kühnert and Sven Wießner in a future research project.

The present study tests the applicability of the viscoelastic Kaye-Bernstein–Kearsley–Zapas (K-BKZ) rheological model to both a pure gum acrylonitrile–butadiene rubber (NBR) as well as a carbon black filled NBR compound. This integral constitutive equation is based on a time- and deformation-dependend polymer network.

First, small amplitude oscillatory shear (SAOS) tests are carried out for the characterization of storage and loss moduli. Second, time-temperature superposition (TTS) is performed to extend the accessible frequency range at the reference temperature. Finally, the steady-state shear and apparent extensional viscosity is calculated from high pressure capillary rheometry (HPCR) data. These rheological properties are subsequently used to fit the viscoelastic K-BKZ (Wagner), the viscoplastic Herschel-Bulkley and the viscous power-law models.

Next, two-dimensional axisymmetric finite element models of three abrubt capillaries and one tapered orifice die are built in the commercial software package ANSYS Polyflow aiming to predict measured pressure drops of the HPCR experiment.

For the unfilled gum NBR the K-BKZ (Wagner) simulation results match experimental data almost perfectly. As expected, the viscous power-law model underestimates pressure drops with an avarage deviation exceeding 38 %.

Adding fillers to a polymer matrix increases the linear viscoelastic moduli but decreases entropy elastic flow phenomena. This behavior is pronounced at high filler loadings (occluded, trapped rubber) especially when adding active particles like carbon black (bound rubber). However, the K-BKZ (Wagner) model is not able to reflect this relation in its current mathematical formulation. To ensure its applicability to highly filled polymer systems: (1) a dependency on the effective filler volume and (2) a (visco)plastic term must be added. This task will be addressed by the groups of Walter Friesenbichler, Evan Mitsoulis, Ines Kühnert and Sven Wießner in a future research project.

Original language | English |
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Publication status | Published - 28 Jun 2021 |

Event | DKG Elastomer Symposium - Duration: 28 Jun 2021 → 1 Jul 2021 |

### Conference

Conference | DKG Elastomer Symposium |
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Period | 28/06/21 → 1/07/21 |