Paper detail

Assessing a Hydrodynamic Description for Instabilities in Highly Dissipative, Freely Cooling Granular Gases

An intriguing phenomenon displayed by granular flows and predicted by kinetic-theory-based models is the instability known as particle &#34;clustering,&#34; which refers to the tendency of dissipative grains to form transient, loose regions of relatively high concentration. In this work, we assess a modified-Sonine approximation recently proposed [Garzó et al., Physica A 376, 94 (2007)] for a granular gas via an examination of system stability. In particular, we determine the critical length scale associated with the onset of two types of instabilities -vortices and clusters- via stability analyses of the Navier-Stokes-order hydrodynamic equations by using the expressions of the transport coefficients obtained from both the standard and the modified-Sonine approximations. We examine the impact of both Sonine approximations over a range of solids fraction ϕ<0.2 for small restitution coefficients e=0.25--0.4, where the standard and modified theories exhibit discrepancies. The theoretical predictions for the critical length scales are compared to molecular dynamics (MD) simulations, of which a small percentage were not considered due to inelastic collapse. Results show excellent quantitative agreement between MD and the modified-Sonine theory, while the standard theory loses accuracy for this highly dissipative parameter space. The modified theory also remedies a (highdissipation) qualitative mismatch between the standard theory and MD for the instability that forms more readily. Furthermore, the evolution of cluster size is briefly examined via MD, indicating that domain-size clusters may remain stable or halve in size, depending on system parameters.