(313a) A Generalized Constitutive Model for Dilute and Semi-Dilute Flexible Polymer Solutions

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 an extension when the molecules are almost fully stretched (FENE-PB model). For uniform concentration systems only the latter part plays a role.

For the dissipative part of the dynamics, non-isotropic mobility effects due to the polymer chain interactions and a dependence of the relaxation time on the polymer chain configurations (according to the extensional/shear characteristics of the flow) are taking into account. Based on the above, two slightly different versions are proposed. Limiting cases are the well-known FENE-P, Oldroyd-B, Giesekus and PTT models.

The characteristics of the new model under simple viscometric flows are presented. It is also used in direct numerical simulations of viscoelastic turbulent channel flow and the results are compared against those obtained with the original FENE-P and Giesekus models.