Abstract
In a recent reformulation of the Marrucci-Ianniruberto constitutive equation for the rheology of entangled polymer melts in the context of nonequilibrium thermodynamics, rather large values of the convective constraint release parameter βccr had to be used in order for the model not to violate the second law of thermodynamics. In this work, we present an appropriate modification of the model, which avoids the splitting of the evolution equation for the conformation tensor into an orientation and a stretching part. Then, thermodynamic admissibility simply dictates that βccr ≥ 0, thus allowing for more realistic values of βccr to be chosen. Moreover, and in view of recent experimental evidence for a transient stress undershoot (following the overshoot) at high shear rates, whose origin may be traced back to molecular tumbling, we have incorporated additional terms into the model accounting, at least in an approximate way, for non-affine deformation through a slip parameter ξ. Use of the new model to describe available experimental data for the transient and steady-state shear and elongational rheology of entangled polystyrene melts and concentrated solutions shows close agreement. Overall, the modified model proposed here combines simplicity with accuracy, which renders it an excellent choice for managing complex viscoelastic fluid flows in large-scale numerical calculations.
Highlights
Using accurate constitutive models to describe the complex rheological response of high molecular weight (MW) polymers to an applied flow field allows for the more economic, rational design of new polymer-based products as well as for the improved description of processing operations as these models are key ingredients in large-scale numerical calculations of viscoelastic fluid flows
When a vanishing value of the anisotropic parameter α is considered, a vanishing second normal stress coefficient is predicted As the convective constraint release (CCR) parameter increases, both η and Ψ1 exhibit a faster shear thinning behavior, which is the expected behavior given that the CCR
While keeping βccr constant, upon increasing the value of α from 0 to 0.1, the power-law exponent at large shear rates changes to −1 and −5/3 for η and Ψ1, respectively
Summary
Using accurate constitutive models to describe the complex rheological response of high molecular weight (MW) polymers (melts or solutions) to an applied flow field allows for the more economic, rational design of new polymer-based products as well as for the improved description of processing operations as these models are key ingredients in large-scale numerical calculations of viscoelastic fluid flows. Chain reptation within the mean-field tube is not a mathematical invention; it has been directly observed in molecular simulations [3]. It is well-known that for the tube model to be able to quantitatively describe the equilibrium dynamics of actual polymeric systems, it has to account for additional mechanisms, such as contour length fluctuations (CLFs) due to the “breathing” motion of chain ends, and constraint release (CR) due to the destruction of topological constraints as a result of the simultaneous (collective) relaxation of the other chains surrounding the reference chain
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