Effect of mass diffusion upon the thermal-diffusive behavior of a dry vibrated granular bed

We report the results of an experimental study on the thermal-diffusion mechanisms of particles with fluctuant motion in a dry granular system. Granular beds with different intensities of particle self-diffusion were produced by exerting vertical vibration-driving forces of different strengths. The effective thermal diffusivity, αe, was determined by solving the inverse transient heat conduction problem. The self-diffusion coefficient in the vertical direction, Dyy, was calculated to describe the diffusive motions of the particles in the bed. The dimensionless Lewis number, Le, was calculated to investigate the relationship between mass diffusion and thermal diffusion. First, we demonstrated that mass diffusion increased the thermal-diffusive behavior of the dry granular system. Second, we identified a positive linear correlation with the specific slope Sαd between αe and Dyy. In particular, the value of Sαd represents a characteristic of the granular system related to the relationship between thermal diffusivity and the mass diffusivity; this means that Le may approach the value of Sαd if the intensity of particle self-diffusion in the bed is sufficiently strong.