Peter P. Mitrano, Vicente Garzó, Andrew M. Hilger, Christopher J. Ewasko, Christine M. Hrenya
An intriguing phenomenon displayed by granular flows and predicted by
kinetic-theory-based models is the instability known as particle "clustering,"
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 [Garz\'o 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 continuum theory 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 \phi <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. 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
(high-dissipation) 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.
View original:
http://arxiv.org/abs/1202.4977
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