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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

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George A.J. Holroyd

Samuel J. Martin

Richard Stuart Graham


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 (?yy) 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
Acceptance Date Jun 9, 2017
Online Publication Date Jul 10, 2017
Deposit Date Jun 14, 2017
Publicly Available Date Jul 10, 2017
Journal Journal of Rheology
Print ISSN 0148-6055
Electronic ISSN 1520-8516
Publisher American Institute of Physics
Peer Reviewed Peer Reviewed
Volume 61
Issue 5
Public URL
Publisher URL


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