Unsteady non-Newtonian hydrodynamics in granular gases

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.

19 pages, 3 tables, 14 figures

References in corpus (9)

• Inherent Rheology of a Granular Fluid in Uniform Shear Flow
• The Boltzmann equation for driven systems of inelastic soft spheres
• The rich behavior of the Boltzmann equation for dissipative gases
• Uniform shear flow in dissipative gases. Computer simulations of inelastic hard spheres and (frictional) elastic hard spheres
• Class of dilute granular Couette flows with uniform heat flux
• Does the Chapman--Enskog expansion for sheared granular gases converge?
• Aging to non-Newtonian hydrodynamics in a granular gas
• Boltzmann equation for dissipative gases in homogeneous states with nonlinear friction
• Computer simulations of an impurity in a granular gas under planar Couette flow

Cited by in corpus (6)

• Linear hydrodynamics for driven granular gases
• Hydrodynamic Burnett equations for inelastic Maxwell models of granular gases
• Time-dependent homogeneous states of binary granular suspensions
• Hydrodynamics of granular particles on a line
• Rheological effects in the linear response and spontaneous fluctuations of a sheared granular gas
• Fluctuations in the Uniform Shear Flow state of a granular gas