A Lagrangian formulation for the Oldroyd B fluid and the second principle of thermodynamics

TL;DR

This paper develops a Lagrangian formulation for the Oldroyd B fluid model, ensuring thermodynamic consistency, and introduces new nonlinear models and formulations for related fluid models, analyzing their thermodynamic compliance.

Contribution

It presents a novel Lagrangian framework for the Oldroyd B model and derives new nonlinear variants and formulations for related fluid models, assessing their thermodynamic validity.

Findings

Oldroyd B model is the Eulerian form of a thermodynamically consistent Lagrangian model.

New nonlinear versions of the Oldroyd B model are derived.

Lagrangian formulations of Zaremba-Jaumann and Oldroyd A models are proposed and analyzed.

Abstract

We show that the Oldroyd B fluid model is the Eulerian form of a Lagrangian model with an internal variable that satisfies the second law of thermodynamics under some conditions on the initial value of the internal variable. We similarly derive several new nonlinear versions of the Oldroyd B model as well as Lagrangian formulations of the Zaremba-Jaumann and Oldroyd A fluid models. We discuss whether or not these other models satisfy the second law.