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Journal Article

A universal scaling law for the evolution of granular gases.

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Hummel,  Mathias
Group Non-equilibrium soft matter, Department of Dynamics of Complex Fluids, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Clewett,  James P. D.
Group Non-equilibrium soft matter, Department of Dynamics of Complex Fluids, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Mazza,  Marco G.
Group Non-equilibrium soft matter, Department of Dynamics of Complex Fluids, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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http://iopscience.iop.org/article/10.1209/0295-5075/114/10002/meta;jsessionid=B33E07E980FC68983354D0A216D667A6.c1.iopscience.cld.iop.org
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Citation

Hummel, M., Clewett, J. P. D., & Mazza, M. G. (2016). A universal scaling law for the evolution of granular gases. Europhysics Letters, 114(1): 10002. doi:10.1209/0295-5075/114/10002.


Cite as: https://hdl.handle.net/11858/00-001M-0000-002A-5142-7
Abstract
Dry, freely evolving granular materials in a dilute gaseous state coalesce into dense clusters only due to dissipative interactions. Here we show that the evolution of a dilute, freely cooling granular gas is determined in a universal way by the ratio of inertial flow and thermal velocities, that is, the Mach number. Theoretical calculations and direct numerical simulations of the granular Navier-Stokes equations show that irrespective of the coefficient of restitution, density or initial velocity distribution, the density fluctuations follow a universal quadratic dependence on the system’s Mach number. We find that the clustering exhibits a scale-free dynamics but the clustered state becomes observable when the Mach number is approximately of O(1). Our results provide a method to determine the age of a granular gas and predict the macroscopic appearance of clusters.