Transverse flow and mixing of granular materials in a rotating cylinder

The focus of this work is analysis of mixing in a rotating cylinder—a prototype system for mixing of granular materials—with the objective of understanding and highlighting the role of flow on the dynamics of the process. The analysis is restricted to low speeds of rotation, when the free surface of the granular solids is nearly flat, and when particles are identical so that segregation is unimportant. The flow is divided into two regions: a rapid flow region of the cascading layer at the free surface, and a fixed bed of particles rotating at the angular speed of the cylinder. A continuum model, in which averages are taken across the layer, is used to analyze the flow in the layer. Good agreement is obtained between the predictions of the flow model for the layer thickness profile and experimental results obtained by digital image analysis. The dynamics of the mixing process are studied by advecting tracer particles by the flow and allowing for particle diffusion in the cascading layer. The mixing model predictions for distribution of tracer particles and mixing rates are compared qualitatively and quantitatively to experimental data. Optimal operating conditions, at which mixing rates are maximum, are determined.

[1]  E. Pohlhausen,et al.  Der Wärmeaustausch zwischen festen Körpern und Flüssigkeiten mit kleiner reibung und kleiner Wärmeleitung , 1921 .

[2]  D. Inman,et al.  Experimental evaluation of a dynamic yield criterion for granular fluid flows , 1985 .

[3]  Prabhu R. Nott,et al.  Frictional–collisional equations of motion for participate flows and their application to chutes , 1990, Journal of Fluid Mechanics.

[4]  Charles S. Campbell,et al.  RAPID GRANULAR FLOWS , 1990 .

[5]  Volkhard Buchholtz,et al.  Simulation of rotating drum experiments using non-circular particles , 1995, cond-mat/0203589.

[6]  R. L. Braun,et al.  Simulation of rotary-drum and repose tests for frictional spheres and rigid sphere clusters , 1993 .

[7]  Douglas W. Fuerstenau,et al.  Transverse mixing in rotating cylinders , 1972 .

[8]  J. Ottino.  The Kinematics of Mixing: Stretching, Chaos, and Transport , 1989 .

[9]  Alex Hansen,et al.  Disorder and granular media , 1993 .

[10]  M. Nakagawa,et al.  Non-invasive measurements of granular flows by magnetic resonance imaging , 1993 .

[11]  J. Williams,et al.  The segregation of particulate materials. A review , 1976 .

[12]  B. White,et al.  Dynamic shear of granular material under variable gravity conditions , 1988 .

[13]  Suresh K. Bhatia,et al.  Axial transport of granular solids in rotating cylinders. Part 2: Experiments in a non-flow system , 1991 .

[14]  Julio M. Ottino,et al.  Mixing of granular materials in slowly rotated containers , 1996 .

[15]  Rajchenbach.  Flow in powders: From discrete avalanches to continuous regime. , 1990, Physical review letters.

[16]  Guy T. Houlsby,et al.  The Flow of Granular Materials-III Rapid Shear Flows , 1983 .

[17]  K. Schügerl,et al.  Transverse mixing and heat transfer in horizontal rotary drum reactors , 1977 .

[18]  J. K. Brimacombe,et al.  Experimental study of transverse bed motion in rotary kilns , 1983 .

[19]  B. Smit,et al.  Commensurate ‘freezing’ of alkanes in the channels of a zeolite , 1995, Nature.

[20]  R. Bagnold.  Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear , 1954, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[21]  R. Jackson,et al.  Frictional–collisional constitutive relations for granular materials, with application to plane shearing , 1987, Journal of Fluid Mechanics.

[22]  I. Inoue,et al.  Motion of Particle and Mixing Process in a Horizontal Drum Mixer , 1970 .

[23]  J. Bridgwater,et al.  Fundamental powder mixing mechanisms , 1976 .