Rational Extended Thermodynamics for Non-Newtonian Fluids with Finite Relaxation Time

TL;DR

This paper develops a hyperbolic, thermodynamically consistent model for non-Newtonian fluids with finite relaxation time, capturing viscoelastic effects and converging to known rheological laws, providing a first-principles alternative to empirical models.

Contribution

It introduces a novel first-principles hyperbolic model within Rational Extended Thermodynamics for non-Newtonian fluids with finite relaxation time.

Findings

Model preserves finite signal speeds and thermodynamic consistency.

Captures viscoelastic phenomena with nonlinear stress evolution.

Converges to power-law rheology in the relaxation limit.

Abstract

We introduce a one-dimensional, hyperbolic model for non-Newtonian fluids with finite relaxation time, derived within the framework of Rational Extended Thermodynamics (RET). Unlike classical parabolic models, our formulation preserves finite signal speeds, thermodynamic consistency, and mathematical well-posedness. The model captures viscoelastic phenomena via a nonlinear evolution of stress, converging to power-law rheology in the vanishing relaxation limit. Notably, it mimics the Phan-Thien-Tanner model under steady shear, but derives from first principles, offering a predictive alternative to empirical rheology.