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Lack of Scale Separation in Granular Flows Driven by Gravity

Author(s): G. Rossi; A. Armanini

Linked Author(s): Aronne Armanini

Keywords: No keywords

Abstract: Since about three decades, granular flows have been studied through the kinetic theories, originally derived for gases: the reason is a certain similarity between granular flows and gases, given that granular collisions can be considered an equivalent of the molecules collisions. However there are important differences between the two applications: in molecular gases the microscale, represented by the mean molecular free paths, is very much smaller than the macroscale, according to which gradients change (Goldhirsch 2003, Goldhirsch2008), while in granular flows driven by gravity the dimension of a single particle becomes comparable to that of the control volume. Statistically speaking, the system is no more ergodic: the averages of a process parameter done over time, over space and over a statistical ensemble do not coincide. For this reason we believe that, instead of the usual ensemble average, a different type of average is needed. A deep analysis of the implications due to the averaging processes applied at different scale must be taken into account. In particular, an intermediate scale will be solved applying a type of average, which accounts for the fluctuations of the number density and leads to additional diffusive terms. The closure relation of the small scale currently adopted in the kinetic theories will be extended to the intermediate scale by scaling the diffusive coefficient according to the square root of the granular temperature and the flow depth h or the particles distance from the wall (instead of the particle diameter d, used for the small scale). A proper definition of the diffusive coefficient will be provided through an intensive experimental investigation.


Year: 2016

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