Mesoscopic constitutive relations for dilute polymer solutions

TL;DR

This paper develops a mesoscopic thermodynamics framework to derive nonlinear constitutive relations for dilute polymer solutions, linking molecular deformation with macroscopic flow behavior and validating models against experiments.

Contribution

It introduces a novel mesoscopic thermodynamics approach to derive coupled hydrodynamic and molecular deformation equations for dilute polymer solutions.

Findings

Derived nonlinear constitutive relations for pressure tensor.

Compared models with experimental data.

Established a mesoscopic nonequilibrium thermodynamics framework.

Abstract

A novel approach to the dynamics of dilute solutions of polymer molecules under flow conditions is proposed by applying the rules of mesoscopic nonequilibrium thermodynamics (MNET). The probability density describing the state of the system is taken to be a function of the position and velocity of the molecules, and on a local vector parameter accounting for its deformation. This function obeys a generalized Fokker-Planck equation, obtained by calculating the entropy production of the system, and identifying the corresponding probability currents in terms of generalized forces. In simple form, this coarse-grained description allows one to derive hydrodynamic equations where molecular deformation and diffusion effects are coupled. A class of non-linear constitutive relations for the pressure tensor are obtained. Particular models are considered and compared with experiments.