Radial mixing of granular materials in a rotating cylinder: experimental determination of particle self-diffusivity

Abstract

Particle self-diffusion has a significant effect on mixing and thus on performance of rotating cylinder systems such as rotary kilns and drum mixers. We study experimentally the radial mixing of monodisperse beads of different colors in a quasi-two-dimensional cylinder rotated in the continuous flow regime. In this regime a shallow surface layer of particles flows steadily while the rest of the material rotates as a solid body. The initial distribution of tracer particles is taken to be radially symmetric and cylinder is taken to be half full. Both facilitate estimation of the particle self-diffusivity since the evolving concentration distribution during mixing in this case is radial for most part and the mixing in these conditions is shown to be dominated by diffusion of particles. A qualitative study of the mixing is carried out using digital photography. Radial number fraction profiles of the tracer particles are obtained by bulk sampling. Since mixing occurs only in the flowing layer, mixing is considered in terms of "passes"defined as the number of times the material in the bed entirely flows through the layer. Experimental results indicate that the mixing per pass decreases with increasing rotational speed, increases with increasing particle size, and is nearly independent of cylinder size. The mixed state captured by digital photography and the measured radial concentration profiles are well described by a convective diffusion model, using diffusivity as a fitting parameter. The diffusivity obtained from the model follows the scaling proposed by Savage [ "Disorder, diffusion, and structure formation in granular flow,"Disorder and Granular Media, edited by A. Hansen and D. Bideau (Elsevier, Amsterdam, 1993), pp. 255-285 ] and a simple expression for the diffusivity is obtained in terms of the particle diameter and the static and dynamic angles of repose.