Long Wavelength Instability for Uniform Shear Flow

TL;DR

This paper demonstrates a long wavelength instability in uniform shear flow using hydrodynamic equations, validated by kinetic theory and Monte Carlo simulations, applicable across different densities.

Contribution

It reveals a long wavelength instability in uniform shear flow through hydrodynamic and kinetic theory analysis, supported by simulation results.

Findings

Hydrodynamic equations show instability at all densities.

Higher order rheological effects influence stability.

Simulation results agree with theoretical predictions.

Abstract

Uniform Shear Flow is a prototype nonequilibrium state admitting detailed study at both the macroscopic and microscopic levels via theory and computer simulation. It is shown that the hydrodynamic equations for this state have a long wavelength instability. This result is obtained first from the Navier-Stokes equations and shown to apply at both low and high densities. Next, higher order rheological effects are included using a model kinetic theory. The results are compared favorably to those from Monte Carlo simulation.