Reversible axial segregation of binary mixtures of granular materials

K. M. Hill, J. Kakalios
1994 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
Measurements of axial segregation of binary mixtures of glass beads having different diameters in a rotating horizontal cylinder are reported. For rotation speeds of ~ 15 rpm a mixed state quickly (within a few minutes) segregates into sharp bands of alternating large and small glass beads along the axis of rotation. Decreasing the rotation speed to ~ 5 rpm causes the bands to disappear, restoring the mixed state. This process is reversible upon increasing the rotation rate, though the exact
more » ... though the exact location and width of the bands vary from run to run. The axial segregation phenomena are analyzed in terms of a diffusion equation where the effective diffusion coefficient is the difference between segregating drift and normal Fickian diffusion. PACS number(s): 46.10.+z, 47.27.Te, 64.75.+g A fascinating property of binary mixtures of granular media such as sand and powders is the phenomenon of mass or size segregation when the mixture is shaken or rotated [1-10]. When a horizontal cylinder is partially filled with a mixture of two different types of granular media, such as different sizes or masses of glass beads or sand, and then rotated about its long axis, the binary mixture segregates into alternating bands of relatively pure single concentrations along the axis of rotation [3-10]. One proposed explanation of this phenomenon, termed axial segregation, involves a diffusion equation for the relative concentrations of the individual species in the mixture, where the ordinary diffusion coefficient is replaced by an effective diffusion coefficient which depends on the relative contributions of normal Fickian diffusion (tending to mix the two species) and a preferential drift term [9] . The drift term arises from a difference between the dynamic angle of repose of the mixed and segregated states. When the drift term is larger than the Fickian diffusion term, fluctuations of separated species grow with time. The phenomenon of axial segregation is well known in the engineering literature and has recently attracted attention as an additional mechanism, other than vertical shaking, by which binary granular mixtures can spatially segregate. While segregation of binary mixtures of granular media, either due to shaking or rotation, is well known, there has been to date no description of a reversible segregation phenomenon. In this paper we report experimental measurements of axial segregation for a binary mixture of glass beads for which the segregated state can be reversed, restoring the mixed state, simply by changing the speed of rotation. Measurements of the dynamic angle of repose φ as a function of the rotation speed confirms that the difference between φ of the mixed and segregated phases varies with the rotation speed, in agreement with our observations of mixing and demixing phenomena. A basis for a statistical mechanics of powders was recently described by Edwards and Mehta [11] . While in a thermodynamic system the energy of the system depends on the configurations of the constituent microscopic particles, for a granular material it is the volume rather than the energy which depends on the configurations of the individual particles.
doi:10.1103/physreve.49.r3610 pmid:9961797 fatcat:pp2qg2emozhs7hkfmfvakmblaq