Hydrodynamics, wall-slip, and normal-stress differences in rarefied granular Poiseuille flow

Area of Science:

• Fluid Dynamics
• Non-Newtonian Rheology
• Granular Materials Science

Background:

• Understanding granular gas flow is crucial for various industrial applications.
• The interplay between particle collisions (inelasticity) and flow rarefaction significantly impacts macroscopic behavior.
• Existing models for molecular gases may not fully capture granular flow complexities.

Purpose of the Study:

• To investigate hydrodynamic fields and rheology in acceleration-driven Poiseuille flow of a dilute granular gas.
• To analyze the competition between dissipation-induced clustering and rarefaction-induced declustering.
• To determine appropriate boundary conditions and rheological models for granular gases across different Knudsen numbers.

Main Methods:

• Direct Simulation Monte Carlo (DSMC) method was employed.
• Simulations covered a range of Knudsen numbers (Kn) from rarefied to transitional flow regimes.
• Phase diagrams were constructed to delineate the influence of inelasticity and rarefaction.

Main Results:

• Dissipation-induced clustering and rarefaction-induced declustering were observed to compete, affecting density profiles.
• Rarefaction-induced temperature bimodality was noted, potentially influenced by inelastic dissipation.
• A modified Maxwell-Navier-type boundary condition was identified, with slip length showing a power-law dependence on Kn (δ≈0.95).
• Normal stress differences exhibited sign changes correlating with density profiles and influenced by rarefaction and inelasticity.

Conclusions:

• The study reveals complex interactions between inelasticity and rarefaction in granular gas flows.
• A modified boundary condition provides a better description for granular Poiseuille flow compared to molecular gas models.
• The findings offer insights into the anomalous behavior of granular gases and the Knudsen paradox.