Investigation of the breakdown of Navier-Stokes equation using Objective Molecular Dynamics

The study examines the flow of Lennard-Jones argon gas under macroscopically uniform shear flow using Objective Molecular Dynamics (OMD). The resulting stress and temperature profiles are compared with corresponding macroscopic profiles derived from Navier-Stokes-Fourier (NSF) continuum mechanics. Agreement between NSF and computational data is found for small shear rates. We also investigate the regime where NSF has limitations in predicting the correct behavior. As an alternative method to achieve better prediction in this regime, we use theory of Rivlin-Ericksen (RE). We propose and calibrate the non-linear RE constitutive model using OMD results. The model is shown to reduce to NSF theory in the limit of low gradient flows and make significant improvement over it under far-from-equilibrium conditions. We also establish the connection between RE and kinetic theory for a gas composed of Maxwellian molecules in simple shear.