(413i) Modeling Dilute and Semi-Dilute Flexible Polymer Solutions in Extensionally-Dominated Flows

Extensionally-dominated flows are of importance in several applications involving dilute and semi-dilute polymer solutions, such as those involving the use of polymer solutions in liquid jets, in flow through porous media in tertiary oil recovery as well as in polymer-induced drag reduction.  Traditionally, dilute polymer solutions are modeled at the continuum level by an entropic spring-type model, such as the Finitely Extensible of Non-linear Elastic dumbbells with the Peterlin approximation (FENE-P) model.  On the other hand, semi-dilute solutions are often modeled by an anisotropic mobility model, such as the Giesekus model.  It is straightforward to also imagine several refinements based on these ideas, such as the use of the inverse Langevin function instead of the Peterlin function to represent finite extensibility effects, or, especially aided by the non-equilibrium thermodynamics formulation [1], by a combination of that with the anisotropic mobility, defining therefore a modified Giesekus model.  This is indeed the more appropriate model for semi-dilute solutions of finite extensibility flexible macromolecules.  In fact, such a model has been proposed and compared favorably against atomistic simulations for unentangled polymer melts [2]. 

In the present work we develop such a model for semidilute polymer solutions and we utilize it for the modeling of the highly extensional flow associated with fast filament stretching in an effort to test the model against the very recent experimental results obtained for such a flow by Tembely et al. [3].  We show there that, if restricted in the modeling (as is typically the case) by the use of one relaxation mode, in addition to the above-mentioned effects, one needs to consider a significant increase to the effective relaxation time taking place during the flow in order to achieve a good fit of the results.  This is in agreement with one of the suggestions offered by that work which, however, only considered constant relaxation time models, resulting in a partial fit of the results.  The implication is that when a significantly truncated model is used, such as a on relaxation mode continuous viscoelastic model, the parameters entering that description are not to be seen as constants, simply connected to the underlying molecular structure, but as effective, renormalized, ones, with a dependence on the flow and/or flow history.  The nature and further modeling of that dependence remains one area of active investigation.

References

[1] Beris A.N. and Edwards B.J., Thermodynamics of Flowing Systems with Internal Microstructure, Oxford U. Press, 1994.

[2] Stephanou P.S., Baig C. and Mavrantzas V.G., J. Rheology, 53:309-337 (2009).

[3] Tembelya M., Vadillo D., Mackley M.R. and Soucemarianadin, A.. J. Rheology, 56:159-183 (2012).