TEMPERATURE OF A GRANULAR MATERIAL FLUIDIZED BY EXTERNAL VIBRATIONS

The scaling for the temperature of a granular material ''fluidized'' b y external vibrations is determined in the Limit where the dissipation of energy in a collision due to inelasticity, or between successive c ollisions due to viscous drag, is small compared to the energy of the particles. An asymptotic scheme is used, where the dissipation of ener gy is neglected in the leading approximation, and the Boltzmann equati on for the system is identical to that for a gas at equilibrium in a g ravitational field. The density variation in the ''fluidized'' materia l is given by the Boltzmann distribution, and the velocity distributio n is given by the Maxwell-Boltzmann distribution. However, the ''tempe rature'' of the material is not specified by thermodynamic considerati ons, but is determined by a balance between the source of energy due t o the vibrating surface and the dissipation of energy. This balance in dicates that the dependence of temperature on the amplitude of the vib rating surface is sensitively dependent on the mechanism of dissipatio n (inelastic collisions or viscous drag), and also on whether the ampl itude function for the velocity of the vibrating surface is symmetric or asymmetric about zero velocity. However, the temperature turns out to have the same functional dependence on the properties of the system in two and three dimensions.