Scaling of Granular Temperature in a Dense Vibrated Granular Bed

Abstract

The granular temperature underpins the kinetic theory of granular flows as well as theories for heat transfer, segregation, erosion, attrition and aggregation in various granular systems. We report granular temperature data of mono-disperse glass particles in a three-dimensional dense granular bed subject to vertical sinusoidal vibrations over a wide range of vibrational conditions as measured by diffusing wave spectroscopy (DWS). The granular temperature was found to scale with the square of the peak vibrational velocity inline with a number of theoretical models and experiments, but a significant correlation was observed between the granular temperature and the acceleration at constant peak velocity. Therefore, a map of granular temperature as a function of the peak vibrational velocity (range of 30 to 55 mm/s) and acceleration (1.8 to 3.4 Γ) is presented for the first time and discussed.