A Parametric Study of Mixing in a Granular Flow a Biaxial Spherical Tumbler

  • Ivan C. Christov
  • Richard M. Lueptow
  • Julio M. Ottino
  • Rob Sturman
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 181)


We report on a computational parameter space study of mixing protocols for a half-full biaxial spherical granular tumbler. The quality of mixing is quantified via the intensity of segregation (concentration variance) and computed as a function of three system parameters: angles of rotation about each tumbler axis and the flowing layer depth. Only the symmetric case is considered in which the flowing layer depth is the same for each rotation. We also consider the dependence on \(\bar{R}\), which parametrizes the concentric spheroids (“shells”) that comprise the volume of the tumbler. The intensity of segregation is computed over 100 periods of the mixing protocol for each choice of parameters. Each curve is classified via a time constant, \(\tau \), and an asymptotic mixing value, bias. We find that most choices of angles and most shells throughout the tumbler volume mix well, with mixing near the center of the tumbler being consistently faster (small \(\tau \)) and more complete (small bias). We conclude with examples and discussion of the pathological mixing behaviors of the outliers in the so-called \(\tau \)-bias scatterplots.


Rotation Rate Tracer Particle Symmetric Case Granular Flow Steel Bead 
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I.C.C. was supported, in part, by a Walter P. Murphy Fellowship from the Robert R. McCormick School of Engineering and Applied Science and by US National Science Foundation grant CMMI-1000469 at Northwestern and by the LANL/LDRD Program through a Feynman Distinguished Fellowship at Los Alamos National Laboratory, which is operated by Los Alamos National Security, L.L.C. for the National Nuclear Security Administration of the U.S. Department of Energy under contract DE-AC52-06NA25396. We thank Stephen Wiggins for suggesting the \(\tau \)-bias scatterplots and useful discussions.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Ivan C. Christov
    • 1
  • Richard M. Lueptow
    • 2
  • Julio M. Ottino
    • 2
  • Rob Sturman
    • 3
  1. 1.Theoretical Division and Center for Nonlinear StudiesLos Alamos National LaboratoryLos AlamosUSA
  2. 2.Department of Chemical and Biological Engineering, Department of Mechanical Engineering and The Northwestern Institute on Complex Systems (NICO)Northwestern UniversityEvanstonUSA
  3. 3.Department of Applied MathematicsUniversity of LeedsLeedsUK

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