Advanced Powder Technol. , Vol. 12, No. 1, pp. 61– 77 (2001) Ó VSP and Society of Powder Technology, Japan 2001. Original paper Self-diffusion analysis in a vibrated granular bed SHIE-CHEN YANG and SHU-SAN HSIAU ¤ Department of Mechanical Engineering, National Central University, Taiwan 32054, ROC Received 28 June 2000; accepted 31 August 2000 Abstract —The inuences of ow parameters on self-diffusion in a vibrated granular bed were studied by simulation and experiment. Employing image processing technology and a particle tracking method, the local displacements and velocities of particles were measured. The self- diffusion coefcients were determined from the history of particles’ diffusive displacements. Discrete element method simulation was performed to calculate the particles’ self-diffusive displacements. The simulation results were compared to the experimental tests. The ow behavior of convection rolls in a vibrated bed occurred by the particles’ self-diffusion induced by the energy input from vertical external vibration. The velocity uctuations, granular temperature and self-diffusions were anisotropic with greatest components in the vertical direction. The dependence of the diffusion coefcients on the dimensionless acceleration amplitude, vibration amplitude, vibration frequency, velocity uctuations, granular temperature, vibration velocity, restitution coefcient and solid fraction are discussed. Keywords: Granular temperature; self-diffusion;solid fraction; vibrated bed; convection. NOMENCLATURE D xx self-diffusion coefcient in the streamwise direction (cm 2 / s) D yy self-diffusion coefcient in the transverse direction (cm 2 / s) c autocorrelation value c x ;c y the corrections of the gray level derivatives in x and y directions d particle diameter (mm) e restitution coefcient i; j pixel coordinates k;k x and k y weighting factors used in (4) N total number of tracers * To whom correspondence should be addressed.