Non-Newtonian corrections to radiative viscosity: Israel-Stewart theory as a viscosity limiter

TL;DR

This paper develops a rigorous theoretical framework for non-Newtonian radiative viscosity corrections, demonstrating that Israel-Stewart theory can accurately model these effects in incompressible flows across various radiative conditions.

Contribution

It provides analytical formulas for transport coefficients and shows how Israel-Stewart theory captures non-Newtonian radiative shear stress features.

Findings

Analytical computation of the Chapman-Enskog series for transport coefficients.

Universal formulas applicable to diverse fluids and radiative processes.

Israel-Stewart theory can model non-Newtonian radiative viscosity with proper shear-heat coupling.

Abstract

Radiation is a universal friction-increasing agent. When two fluid layers are in relative motion, the inevitable exchange of radiation between such layers gives rise to an effective force, which tries to prevent the layers from sliding. This friction is often modeled as a Navier-Stokes shear viscosity. However, non-Newtonian corrections are expected to appear at distances of about one optical depth from the layers' interface. Such corrections prevent the viscous stress from becoming too large. Here, we set the foundations of a rigorous theory for these corrections, valid along incompressible flows. We show that, in the linear regime, the infinite Chapman-Enskog series can be computed analytically, leading to universal formulas for all transport coefficients, which apply to any fluid, with any composition, with radiation of any type (also neutrinos), and with nearly any type of radiative process. We then show that, with an appropriate shear-heat coupling coefficient, Israel-Stewart theory can correctly describe most non-Newtonian features of radiative shear stresses.