Inertial theories for dilute viscoelastic polymer blends with a volume preserving microstructure

Abstract

The rheology, microstructure, and non-Newtonian fluid mechanics of dilute immiscible polymer blends are investigated. To derive thermodynamically consistent flow equations for these materials, the Hamiltonian framework of non-equilibrium Thermodynamics is adopted. For a given set of non-equilibrium variables, this formalism allows to derive a set of local rate equations from a Poisson bracket, a dissipation bracket, and a Hamiltonian functional. Flow equations for polymer blends with inertia are developed and the theory is reduced to a set of flow equations without inertia. Furthermore, the viscosity coefficients of the non-inertial theory (coarser level of description) are expressed in terms of the viscosity coefficients of the inertial theory (finer level of description). It is shown that non-equilibrium Thermodynamics allows to derive local rate equations for materials as complex as polymer blends and that non-equilibrium Thermodynamics allows to coarse or fine grain between several levels of description. Finally, it is explained how the flow equations derived herein can be applied to describe polymer blend flow and single droplet deformation in flow geometries which are so small to influence the microstructural dynamics and in particular the droplet dynamics in polymer blends.