Developing a Non-Newtonian Fluid Model for Dust, for Application to Astrophysical Flows

TL;DR

This paper develops a covariant fluid model for collisionless dust in astrophysics, capturing anisotropic stresses and rheological properties, improving the realism of dust flow simulations in turbulent gas environments.

Contribution

It introduces a novel covariant dust fluid model derived from individual grain dynamics, incorporating anisotropic stresses and a higher-dimensional Maxwell fluid analogy.

Findings

The model captures anisotropic pressure effects in dust flows.

It simplifies the constitutive relation for dust rheological stress.

The approach is applicable to accretion disc scenarios.

Abstract

In the astrophysics community it is common practice to model collisionless dust, entrained in a gas flow, as a pressureless fluid. However a pressureless fluid is fundamentally different from a collisionless fluid - the latter of which generically possess a non-zero anisotropic pressure or stress tensor. In this paper we derive a fluid model for collisionless dust, entrained in a turbulent gas, starting from the equations describing the motion of individual dust grains. We adopt a covariant formulation of our model to allow for the geometry and coordinate systems prevalent in astrophysics, and provide a closure valid for the accretion disc context. We show that the continuum mechanics properties of a dust fluid corresponds to a higher-dimensional anisotropic Maxwell fluid, after the extra dimensions are averaged out, with a dynamically important rheological stress tensor. This higher-dimensional treatment has the advantage of keeping the dust velocity and velocity of the fluid seen, and their respective moments, on the same footing. This results in a simplification of the constitutive relation describing the evolution of the dust Rheological stress.