Conformal higher-order viscoelastic fluid mechanics

TL;DR

This paper develops a covariant framework for conformal higher-order viscoelastic fluids, analyzing their dynamics, relaxation times, and connection to fluid/gravity correspondence, ensuring thermodynamic consistency.

Contribution

It introduces a general covariant formulation for conformal higher-order viscoelastic fluids with large strains, linking second-order fluid behavior to viscoelastic models without violating thermodynamic principles.

Findings

Derived a covariant dynamical prescription consistent with thermodynamics.

Showed that second-order conformal fluids can emerge as long-time limits of viscoelastic systems.

Analyzed relaxation times and their relation to velocity gradients.

Abstract

We present a generally covariant formulation of conformal higher-order viscoelastic fluid mechanics with strain allowed to take arbitrarily large values. We give a general prescription to determine the dynamics of a relativistic viscoelastic fluid in a way consistent with the hypothesis of local thermodynamic equilibrium and the second law of thermodynamics. We then elaborately study the transient time scales at which the strain almost relaxes and becomes proportional to the gradients of velocity. We particularly show that a conformal second-order fluid with all possible parameters in the constitutive equations can be obtained without breaking the hypothesis of local thermodynamic equilibrium, if the conformal fluid is defined as the long time limit of a conformal second-order viscoelastic system. We also discuss how local thermodynamic equilibrium could be understood in the context of the fluid/gravity correspondence.