Diffusive and subdiffusive axial transport of granular material in rotating mixers

Abstract

The segregation of granular mixtures in rotating cylinders into axial bands is not well understood so far. Abnormal diffusion of the grains has been proposed to play an important role in that process. We measure axial diffusion in binary mixtures, completely embedded in water, by means of nuclear magnetic imaging (magnetic resonance imaging). It is found that the small size particles in a radially segregated structure undergo normal (Fickian) axial diffusion, whereas an initial pulse of the large species shows subdiffusive behavior. An interpretation within a model for the particle dynamics is given. The diffusion of small particles occurs in the axial kernel, whereas particles of the large species migrate on the free surface of the granular bed.

Resolving a paradox of anomalous scalings in the diffusion of granular materials

“…Nevertheless, a concentration-dependent axial diffusivity with Dð0Þ ¼ 0 (as in refs. (11,36)) is not consistent with the theory of the monodisperse case because, even in the absence of small particles, the large particles self diffuse (and vice versa). In light of the discussion in ref.…”

“…Neither experiments (35,36) nor DEM simulations (34, 37) provide sufficiently well resolved data to determine the functional form of DðCÞ with any certainty or whether to pick the "þ" or "−" sign in the proposed expression. Nevertheless, a concentration-dependent axial diffusivity with Dð0Þ ¼ 0 (as in refs.…”

“…In light of the discussion in ref. (36), the form DðCÞ ¼ 1 AE ðC − 1∕2Þ can be reinterpreted: if C ¼ C l is the concentration of large particles then the "þ" sign should be chosen because a locally higher than average concentration of large particles leads to enhanced lateral diffusivity beyond that of a perfect mixture (C ¼ 1∕2) for all nearby particles. Meanwhile, the opposite must be true for the concentration of small particles, namely…”

“…(11) because it possesses an exact self-similar solution of the form cðz; tÞ ¼ Cðz∕t α Þt −α with α ¼ 1∕3 < 1∕2 (38,39). On this basis, it has been argued (36,40) that concentration-dependent diffusivity of this form could explain the anomalous scalings in ref. (11), at least for bidisperse mixtures.…”

“…Another set of experiments (35,36) and DEM simulations (37) have provided some evidence for a concentration-dependent diffusivity in bidisperse mixtures, i.e., granular materials consisting of two kinds of particles differing either in size, density, shape, roughness, etc. Specifically, it was found that that a band of larger particles diffuses anomalously in a background of smaller particles.…”