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Derivation of Two-Fluid Model Based on Onsager Principle.

Jiajia Zhou^1,2, Masao Doi^3,4

¹South China Advanced Institute for Soft Matter Science and Technology, School of Emergent Soft Matter, South China University of Technology, Guangzhou 510640, China.

Entropy (Basel, Switzerland)

|May 28, 2022

Summary

This study explores polymer solutions using the Onsager variational principle, deriving dynamic equations for polymer stress and composition coupling. It provides a constitutive equation, improving upon the Doi-Onuki two-fluid model.

Keywords:

Onsager principle dynamics of polymer solution two-fluid model

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Area of Science:

Polymer Physics
Rheology
Statistical Mechanics

Background:

The Doi-Onuki two-fluid model requires a constitutive equation for polymer stress.
Previous work established a dumbbell model for homogeneous viscoelastic fluids.

Purpose of the Study:

To investigate the dynamic coupling between stress and composition in polymer solutions.
To derive a constitutive equation for polymer stress using the Onsager variational principle.

Main Methods:

Application of the Onsager variational principle.
Utilizing a dumbbell model for polymer chains.
Derivation of dynamic equations from first principles.

Main Results:

Successfully derived dynamic equations governing polymer stress and composition coupling.
Provided a closure relation (constitutive equation) for the polymer stress.
Established a theoretical framework based on the Onsager variational principle.

Conclusions:

The Onsager variational principle offers a robust method for deriving polymer solution dynamics.
This approach overcomes limitations of a priori assumptions in existing models.
The derived constitutive equation enhances the predictive capability of polymer fluid theories.