Abstract
A 1d Boltzmann equation is introduced to describe the speed distribution function in granular gas system with local collision dissipation. It leads to introduce a new term, equivalent to an acceleration This term was always assumed to be 0, but it is not zero in general, even when the system is steady (i.e. when local mean flow equals 0). This shows that the flow (+ boundary) exerts a force on any extra steady particle (or plane) that drives it to the center. This result is analyzed, compared and interpreted using the Lagrangian & Eulerian view points of the mechanics; it demonstrates that classic view point of hydrodynamics does not hold anymore. The paper investigates different cases and gives experimental evidences of the features: it explains while local speed distribution f(v,r) of granular gas in a box subjected to vibration is non symmetric in the direction of vibration, while the system is stationary (mean local speed equals 0). Papers giving local experimental or simulated distributions are quoted, where two local pressures P± = Σv>0,orv<0 (mv2) in +Ox and −Ox direction are different. It implies also introducing two local temperatures T± in the ±Ox vibration direction. These points are confirmed using 2d and 3d granular gas simulation. It should apply likely to get deeper understanding of different effects as the "granular Leidenfrost effect", the stoppage of vibrated-hourglass, some turbulent flow, and the granular-Maxwell-demon.
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