A Taylor vortex analogy in granular flows

Fluids sheared between concentric rotating cylinders undergo a series of three-dimensional instabilities. Since Taylor's archetypal 1923 study, these have proved pivotal to understanding how fluid flows become unstable and eventually undergo transitions to chaotic or turbulent states. In contrast, predicting the dynamics of granular systems—from nano-sized particles to debris flows—is far less reliable. Under shear these materials resemble fluids, but solid-like responses, non-equilibrium structures and segregation patterns develop unexpectedly. As a result, the analysis of geophysical events and the performance of largely empirical particle technologies might suffer. Here, using gas fluidization to overcome jamming, we show experimentally that granular materials develop vortices consistent with the primary Taylor instability in fluids. However, the vortices observed in our fluidized granular bed are unlike those in fluids in that they are accompanied by novel mixing–segregation transitions. The vortices seem to alleviate increased strain by spawning new vortices, directly modifying the scale of kinetic interactions. Our observations provide insights into the mechanisms of shear transmission by particles and their consequent convective mixing.

[1]  H. Pak,et al.  CONVECTION AND SIZE SEGREGATION IN A COUETTE FLOW OF GRANULAR MATERIAL , 1997 .

[2]  Onset of instability in sheared gas fluidized beds , 1997 .

[3]  James O. Wilkes,et al.  Fluid Mechanics for Chemical Engineers , 1998 .

[4]  Harry L. Swinney,et al.  Flow regimes in a circular Couette system with independently rotating cylinders , 1986, Journal of Fluid Mechanics.

[5]  Richard M. Lueptow,et al.  Spatio-temporal character of non-wavy and wavy Taylor–Couette flow , 1998, Journal of Fluid Mechanics.

[6]  James N. Michaels,et al.  Toward rational design of powder processes , 2003 .

[7]  Particle dynamics in sheared granular matter , 2000, Physical review letters.

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

[9]  Heinrich M. Jaeger,et al.  Signatures of granular microstructure in dense shear flows , 2000, Nature.

[10]  Fernando J. Muzzio,et al.  A quantitative image analysis method for characterizing mixtures of granular materials , 1996 .

[11]  P. J. King,et al.  Spontaneous Air-Driven Separation in Vertically Vibrated Fine Granular Mixtures , 2002, Science.

[12]  Y. Forterre,et al.  Longitudinal vortices in granular flows. , 2001, Physical review letters.

[13]  T. Mullin,et al.  Transition to oscillatory motion in the Taylor experiment , 1980, Nature.

[14]  T. Shinbrot,et al.  Nonequilibrium Patterns in Granular Mixing and Segregation , 2000 .

[15]  S. Savage,et al.  Stresses developed by dry cohesionless granular materials sheared in an annular shear cell , 1984, Journal of Fluid Mechanics.

[16]  D. Blackmore,et al.  IUTAM Symposium on Segregation in Granular Flows , 2000 .

[17]  Julio M. Ottino,et al.  Mixing and Segregation of Granular Materials , 2000 .

[18]  D. C. Rapaport,et al.  Molecular Dynamics Simulation of Taylor-Couette Vortex Formation , 1998 .

[19]  Howard H. Hu,et al.  Particle motion in a liquid film rimming the inside of a partially filled rotating cylinder , 2003, Journal of Fluid Mechanics.

[20]  B. Ackerson,et al.  Pattern formation in a rotating suspension of non-Brownian settling particles. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  John Bridgwater,et al.  The dynamics of granular materials – towards grasping the fundamentals , 2003 .

[22]  G. Taylor Stability of a Viscous Liquid Contained between Two Rotating Cylinders , 1923 .

[23]  Benjamin J. Glasser,et al.  Density waves and coherent structures in granular Couette flows , 2004 .

[24]  T. Mullin Mutations of steady cellular flows in the Taylor experiment , 1982, Journal of Fluid Mechanics.

[25]  G. Pfister,et al.  Transient dynamics at the onset of Taylor vortices , 2003, Journal of Fluid Mechanics.

[26]  D. H. Fruman,et al.  Bubble capture and migration in Couette–Taylor flow , 1999 .

[27]  Roy Jackson,et al.  Fluid Mechanical Description of Fluidized Beds. Convective Instabilities in Bounded Beds , 1974 .

[28]  D. R. Scott,et al.  Seismicity and stress rotation in a granular model of the brittle crust , 1996, Nature.