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cooling flow simulation granular flow granular materials integro-differential equations nonlinear differential equations particle size rarefied fluid dynamics temperature distribution homogeneous cooling state kinetic-theory transport-coefficients statistical-mechanics binary-mixtures low-density dynamics media flow particle
Abstract:
A highly polydisperse granular gas is modeled by a continuous distribution of particle sizes,
a
, giving rise to a corresponding continuous temperature profile,
T
(
a
)
, which we compute approximately, generalizing previous results for binary or multicomponent mixtures. If the system is driven, it evolves toward a stationary temperature profile, which is discussed for several driving mechanisms in dependence on the variance of the size distribution. For a uniform distribution of sizes, the stationary temperature profile is nonuniform with either hot small particles (constant force driving) or hot large particles (constant velocity or constant energy driving). Polydispersity always gives rise to non-Gaussian velocity distributions. Depending on the driving mechanism the tails can be either overpopulated or underpopulated as compared to the molecular gas. The deviations are mainly due to small particles. In the case of free cooling the decay rate depends continuously on particle size, while all partial temperatures decay according to Haff’s law. The analytical results are supported by event driven simulations for a large, but discrete number of species.
