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Mechanics of collisional motion of granular materials. I: General hydrodynamic equations. (English) Zbl 0881.76010

Collisional motion of a granular material composed of rough inelastic spheres is analysed on the basis of the kinetic Boltzmann-Enskog equation. The Chapman-Enskog method for gas kinetic theory is modified to derive the Euler-like hydrodynamic equations for a system of moving spheres, possessing constant roughness and inelasticity. The existence of the hydrodynamic state of evolution of a granular medium, where the Euler-like equations are valid, is delineated in terms of the particle roughness and restitution coefficients.
It is shown that the hydrodynamic Euler-like equation, which describes the transport and evolution of the kinetic energy of particle random motion, contains energy sink terms of two types: (i) the term representing energy losses in incompressibly flowing gas; (ii) the term accounting for kinetic energy loss (or gain) associated with the work of pressure forces, leading to gas compression (or expansion). The speed of sound waves propagating in a granular gas is analysed in the limits of low and high granular gas densities. The authors show that the particle collisional properties strongly affect the speed of sound in dense granular media.

MSC:

76A99 Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
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