A universal scaling law for the evolution of granular gases. (22nd April 2016)

• Record Type: Journal Article
• Authors: Hummel, Mathias; Clewett, James P. D.; Mazza, Marco G.
• Is Part Of: Europhysics letters. Volume 114:Number 1(2016:Apr.)
• Publication Date: 2016-04-22
• Subjects: 05.20.-y -- 45.70.Qj -- 47.20.-k; Physics -- Periodicals; Electronic journals; 530.05
• DOI: 10.1209/0295-5075/114/10002
• Languages: English
• ISSNs: 0295-5075

Abstract

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 . Our results provide a method to determine the age of a granular gas and predict the macroscopic appearance of clusters.