# Thermodynamics of viscoelastic rate-type fluids with stress diffusion

## TL;DR

This paper develops thermodynamically consistent models for viscoelastic fluids with stress diffusion, exploring their implications for stability and thermomechanical coupling.

## Contribution

It introduces new variants of Maxwell/Oldroyd-B models with stress diffusion, grounded in thermodynamic principles, and analyzes their stability and physical interpretations.

## Key findings

- Stress diffusion can be linked to nonlocal energy storage or entropy production.
- Models enable analysis of thermomechanical stability in viscoelastic fluids.
- New models facilitate studies of coupled thermomechanical problems.

## Abstract

We propose thermodynamically consistent models for viscoelastic fluids with a stress diffusion term. In particular, we derive variants of compressible/incompressible Maxwell/Oldroyd-B models with a stress diffusion term in the evolution equation for the extra stress tensor. It is shown that the stress diffusion term can be interpreted either as a consequence of a nonlocal energy storage mechanism or as a consequence of a nonlocal entropy production mechanism, while different interpretations of the stress diffusion mechanism lead to different evolution equations for the temperature. The benefits of the knowledge of the thermodynamical background of the derived models are documented in the study of nonlinear stability of equilibrium rest states. The derived models open up the possibility to study fully coupled thermomechanical problems involving viscoelastic rate-type fluids with stress diffusion.