A Generalized Constitutive Model for Dilute and Semi-Dilute Flexible Polymer Solutions

摘要

A new generalized, macroscopic constitutive model suitable for dilute and semi-dilute flexible polymer solutions is presented. As in the FENE-P model the finite extensibility for the polymer macromolecules is explicitly taken into account in the boundness of the internal structural parameter, the conformation tensor. In this model, the extended Helmholtz free energy of the system is decomposed in a thermodynamic equilibrium and a non-equilibrium component. The former, represented mixing, consists of the statistical distribution of the polymer chain size around their average value and the standard Flory-Huggins free energy density for polymer solutions. The latter, assumed purely entropic, is described through the inverse Langevin function based on the bead-rod Kuhn chain model, with a possible extension when the molecules are almost fully stretched (FENE-PB model). For uniform concentration systems only the latter part plays a role.