Ž . Powder Technology 116 2001 224–231 www.elsevier.comrlocaterpowtec Computational approaches to granular segregation in tumbling blenders Troy Shinbrot b , Marco Zeggio a,b , Fernando J. Muzzio b, ) a UniÕersita di PadoÕa, Istituto di Impianti Chimici, 35131 PadoÕa, Italy ´ b Department of Chemical and Biochemical Engineering, Rutgers UniÕersity, Piscataway, NJ 08854 USA Received 3 April 2000; received in revised form 10 September 2000; accepted 20 September 2000 Abstract Ž . We discuss cellular automata CA simulations of granular segregation in several different tumbling blenders, including simple rotating drums, V-blender shells, drums tumbling end-over-end and double-cones. In all cases, simplified CA generates data that agree surprisingly well with companion experiments. This implies that a predictive understanding of segregation mechanisms in a wide variety of problems may be achievable using relatively simple algorithms. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Granular segregation; Tumbling blenders; Cellular automata simulations 1. Introduction An ubiquitous property of granular materials is the tendency for blends of dissimilar grains to unmix, or ‘segregate’. Predictive modeling of segregation is hindered by a lack of generally applicable equations for granular flows. In the companion field of fluid mechanics, analytic models can be relied upon because the response of simple fluids to stress can be spatially uniform and history inde- pendent. Granular responses to stress, on the other hand, are typically both strongly nonuniform and history depen- Ž dent except for special cases, e.g. homogeneous rapid . flows , and consequently generic differential equations for powders and grains seem unattainable. For this reason, to study these materials it is necessary to develop alternatives to analytic methods. The most direct approach to simulating granular flows is to track large numbers of individual grains by simultane- ously solving Newton’s laws for each grain. Several differ- ent types of ‘particle-dynamic’ simulations of granular flows have been developed over the course of the last three w x decades 1–10 and have been shown to produce good agreement with experimental data. Computations of this ) Corresponding author. Tel.: q 1-732-445-6710; fax: q 1-732-445- 6758. Ž . E-mail address: shinbrot@sol.rutgers.edu F.J. Muzzio . kind provide a wealth of data that can, in principle, be used to analyze empirical granular phenomena including w x segregation 11,12 , which is the focus of the present paper. Although the quantity of data obtainable from direct simulations can be tremendous, in practice, beyond phe- nomenological duplication of physical experiments, there is seldom a straightforward process for making sense of the data to improve our understanding of the root mecha- nisms leading to segregation. Consequently, developing useful and predictive models remains a long-term goal. For Ž this reason combined with the computational burden of full blown particle-dynamic simulations of tens of thou- . sands of grains , several groups have developed cellular Ž . w x w x automata CA 13–15 , dynamical systems 16–22 , con- w x tinuum 23–26 , and other approaches to granular model- ing. In this paper, we describe results of some of these methods applied to the problem of granular segregation in several tumbling blender geometries. 2. Experimentally validated cellular-automata modeling in a family of tumbling blenders It is axiomatic that in order for segregation to occur, it Ž . is necessary though not sufficient that the velocities of the distinct species of particles making up the blend must w x differ at some point in their history 27,28 . To understand the mechanisms of segregation, we examine practical con- 0032-5910r01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. Ž . PII: S0032-5910 00 00394-6