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Research Activities > Programs > Complex Fluids 2007

Modeling Strong Extensional Flows of Polymer Solutions and Melts

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Modeling Strong Extensional Flows of Polymer Solutions and Melts


Professor Antony Beris

University of Delaware 

Abstract:  Constitutive models for polymeric flows have been traditionally based on the Gaussian approximation assumption about the form of the distribution function dictating the conformation of polymer chains. However, although this is a fairly good approximation near equilibrium, it becomes consistently worst at high levels of extension when the chain distribution is fairly degenerate. The use of a maximum extensibility (in the form used in a traditional FENE-P like model) does not improve this situation---it actually makes it worst! Thus, as an artifact of this approximation, we have the paradox of an estimated extended free energy that becomes infinite in the limit of perfect chain extension. These observations are not limited to dilute polymer solutions but also hold for polymer melts where the role of individual chains is replaced by that of chain segments between entanglements. In fact, a new NonEquilibrium Microscopic Lattice-based Monte Carlo technique that we have recently developed within our research group has been used in a nonequilibrium multiscale simulation to develop a new, thermodynamically consistent, constitutive model correcting the FENE-P expression for free energy (so called FENE-PB --- B standing for Bounded Free Energy) at high levels of extension. The model restores the consistency between the microscopic simulations and the macroscopic estimates for a dense amorphous phase (modeled by a Phan Thien and Tanner equation using the FENE-PB model to account for finite extensibility and a bounded free energy) quite a lot---up to the point where excluded volume effects are important. This new approximation can therefore be used under a variety of situations and it is expected to produce significant differences when there is a significant chain extension.

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