Temperature of a granular gas with regard to the stochastic nature of particle interactions
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| Number of Parts | 63 | |
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| License | CC Attribution 3.0 Unported: You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. | |
| Identifiers | 10.5446/39047 (DOI) | |
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00:00
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Transcript: English(auto-generated)
00:03
Granular materials are systems of dissipatively interacting macroscopic particles. In a regime known as a granular gas, the individual grains interact mainly by instantaneous binary collisions. Due to the inelastic nature of the collisions, the system loses energy,
00:23
which is expressed by the decay in time of the granular temperature, defined as the mean internal free energy per particle. The evolution of a first free granular gas passes through several stages. After a fast kinetic regime, the system converges to its typical velocity distribution,
00:45
which describes the so-called homogeneous cooling state. The temperature decreases due to dissipative collisions, while the system remains spatially homogeneous. Later, local density fluctuations may lead to the spontaneous formation of clusters,
01:00
which may become unstable depending on the particle interactions. In our paper, we are interested in the decay of temperature and the homogeneous cooling state. The cooling of a granular gas depends on the particle interaction model of the system. The inelastic nature of the collisions is characterized by a coefficient of normal restitution,
01:22
defined as the ratio of the normal component of the relative velocities before and after collision. Standard descriptions of granular gases consider constant coefficients of restitution, leading to a cooling behavior known as Hough's law, or viscoelastic particles yielding a different cooling law.
01:41
Recently, it has been shown in experiments, as well as in simulations, that the coefficient of normal restitution describing the collision of rough spheres reveals a stochastic nature that can be described by a double exponential probability density. Here we see histograms of the coefficient of restitution for different impact velocities
02:01
obtained by experiments of particle impacts of a rough spherical particle. We show by means of kinetic theory and simulations that the cooling behavior for these particles deviates from Hough's law, as well as from the expression for viscoelastic particles. Although the deviation from the viscoelastic case is very small,
02:22
the stochastic nature has a clear impact on the system dynamics.