Derivation of Two-fluid Model Based on Onsager Principle

TL;DR

This paper derives a two-fluid model for polymer solutions using the Onsager variational principle, providing a systematic approach to coupling stress and composition dynamics without assuming polymer stress a priori.

Contribution

It introduces a derivation of the two-fluid model based on the Onsager principle, starting from a dumbbell model, which clarifies the dynamic coupling in polymer solutions.

Findings

Derived all dynamic equations from the Onsager principle.

Provided a systematic derivation avoiding a priori stress assumptions.

Connected microscopic dumbbell model to macroscopic two-fluid dynamics.

Abstract

Using Onsager variational principle, we study the dynamic coupling between the stress and the composition in polymer solution. In the original derivation of the two-fluid model [Doi and Onuki, J. Phys. II France {\bf 2}, 1631 (1992)], the polymer stress was introduced \emph{a priopri}, therefore a constitutive equation is required to close the equations. Based on our previous study of viscoelastic fluids with homogeneous composition [Phys. Rev. Fluids {\bf 3}, 084004 (2018)], we start with a dumbbell model for the polymer, and derive all dynamic equations using the Onsager variational principle.