# On diffusive variants of some classical viscoelastic rate-type models

## TL;DR

This paper develops a thermodynamically consistent framework for adding stress diffusion to classical viscoelastic models, enabling more accurate modeling of complex fluid flows with stress diffusion effects.

## Contribution

It introduces a method to incorporate stress diffusion into standard viscoelastic models while maintaining thermodynamic consistency, expanding their applicability.

## Key findings

- Models with stress diffusion obey thermodynamic laws.
- Framework applicable to multiple classical viscoelastic models.
- Potential for improved flow simulations of complex fluids.

## Abstract

We present a thermodynamically based approach to the design of models for viscoelastic fluids with stress diffusion effect. In particular, we show how to add a stress diffusion term to some standard viscoelastic rate-type models (Giesekus, FENE-P, Johnson--Segalman, Phan-Thien--Tanner and Bautista--Manero--Puig) so that the resulting models with the added stress diffusion term are thermodynamically consistent in the sense that they obey the first and the second law of thermodynamics. We point out the potential applications of the provided thermodynamical background in the study of flows of fluids described by the proposed models.