Unsteady non-Newtonian hydrodynamics in granular gases

TL;DR

This paper investigates the unsteady hydrodynamics of dilute granular gases under different flow conditions using simulations, revealing a two-stage evolution from initial state dependence to a non-Newtonian hydrodynamic regime.

Contribution

It demonstrates the existence of a two-stage evolution in granular gases and provides an analytical description of rheological functions during the hydrodynamic stage.

Findings

Identification of a kinetic stage followed by a hydrodynamic stage

Simulation data support the two-stage scenario

Analytical model accurately describes rheological functions

Abstract

The temporal evolution of a dilute granular gas, both in a compressible flow (uniform longitudinal flow) and in an incompressible flow (uniform shear flow), is investigated by means of the direct simulation Monte Carlo method to solve the Boltzmann equation. Emphasis is laid on the identification of a first "kinetic" stage (where the physical properties are strongly dependent on the initial state) subsequently followed by an unsteady "hydrodynamic" stage (where the momentum fluxes are well-defined non-Newtonian functions of the rate of strain). The simulation data are seen to support this two-stage scenario. Furthermore, the rheological functions obtained from simulation are well described by an approximate analytical solution of a model kinetic equation.