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Analytic solutions of the Rolie Poly model in time-dependent shear

Holroyd, George A.J.; Martin, Samuel J.; Graham, Richard Stuart

Authors

George A.J. Holroyd

Samuel J. Martin

Richard Stuart Graham



Abstract

We consider shear flows that comprise of step changes in the shear rate. For these flows, we derive analytic solutions of the Rolie-Poly constitutive equation. Our method involves piecing together solutions for constant rate shear in a variety of flow rate regimes. We obtain solutions for interrupted shear, recoverable strain and non-linear relaxation following cessation of flow. Whenever strong flow is present we neglect reptation, as other mechanisms dominate and for interrupted shear our solution is approximate as we neglect convective constraint release. Our analytic solutions provide new insight in several ways. These include revealing the mechanism of some experimental features of these flows; suggesting a method to extract the polymer contribution to the normal stress in the velocity gradient direction (σyy) from shear stress measurements alone; and a method to isolate the influence of convective constraint release (CCR) from damping function measurements. We also run complementary GLaMM model calculations to verify that insight from our analytic approach translates to this more detailed model.

Journal Article Type Article
Journal Journal of Rheology
Print ISSN 0148-6055
Electronic ISSN 1520-8516
Publisher AIP Publishing
Peer Reviewed Peer Reviewed
Volume 61
Issue 5
APA6 Citation Holroyd, G. A., Martin, S. J., & Graham, R. S. (in press). Analytic solutions of the Rolie Poly model in time-dependent shear. Journal of Rheology, 61(5), doi:10.1122/1.4990639
DOI https://doi.org/10.1122/1.4990639
Publisher URL http://sor.scitation.org/doi/10.1122/1.4990639
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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