Scaling of granular temperature in vibro-fluidized grains

Granular temperature quantifies velocity fluctuations in fluidized granular materials. There is ongoing effort to understand granular temperature T in vibro-fluidized grains through the power law T ∝ V p α , where Vp is peak vibrational velocity. However, the present literature disagrees on the value of α. We utilize dimensional analysis and discrete element simulations to show that granular temperature, and therefore the exponent α, depends crucially on a non-dimensional number W representing the competition between vibrational and gravitational energies but is much less sensitive to other system parameters. Furthermore, change in the barycentric height Δhcm of the vibrated grains, and their temperature T, typically behaves differently with Vp . Thus, Δhcm cannot generally be used as a surrogate for T, as is often done at present. Our computations help explain the currently contradictory results on how granular temperature scales with peak vibrational velocity. Finally, we also briefly investigate the dependence of the temperature on system parameters, as well as its spatial variation.