Substructural interactions and transport in polymer flows

Abstract

A model for semidilute polymer flows is developed within the setting of multifield theories describing material substructures. We associate a coarse grained order parameter to the family of polymer chains in each material element and account for substructural interactions which develop power in the rate of the order parameter and are balanced. A measure of substructural interactions occurring between neighboring families of polymeric chains is prescribed first; then we find the need of the existence of self-interactions in each family by means of a requirement of invariance of the power. We obtain balance equations that involve terms that stabilize numerical algorithms in turbulent regime. Versions of the standard dumbbell model, that fit experimental data, seem to fall within our modeling. Moreover, we obtain evolution equations which are sufficiently flexible to be applied to different (even non-standard) cases. In fact, we make distinction between the balance of (standard and substructural) interactions and their representation. Then, such a representation is a consequence of the prescription of two ingredients: the explicit form of the bulk free energy density and appropriate ‘viscous’ coefficients. The transport of polymer chains between neighboring material elements is also discussed.