A positron emission particle tracking investigation of the flow regimes in tumbling mills

Using positron emission particle tracking (PEPT) data we recover key granular rheology ingredients (velocity, shear rate, volume concentration, bed depth) for developing, testing and calibrating granular flow models. In this regard, 5 mm glass beads were rotated within a 476 mm diameter mill fitted with angled lifter bars along the inner azimuthal walls and operated in batch mode across a range of drum rotation speeds that span cascading and cataracting Froude regimes. After averaging the PEPT outputs into representative volume elements, subsequent continuum analysis of the flowing layer revealed a rich coexistence of flow regimes: a quasi-static layer dominated by frictional interactions, a dense, liquid-like layer that is stressed by frictional and collisional interactions, and an inertial layer that interacts mainly through collisions. Combining the inertial number with an empirically formulated dilatancy law and the measured granular rheological ingredients then facilitated the recovery of the total depth-dependent pressure of the free surface layer.

[1]  Y. Forterre,et al.  Flows of Dense Granular Media , 2008 .

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

[3]  Schofield,et al.  Three-dimensional direct imaging of structural relaxation near the colloidal glass transition , 2000, Science.

[4]  Cheng-Hsien Lee,et al.  Kinetic-theory-based model of dense granular flows down inclined planes , 2012 .

[5]  B. Dubrulle,et al.  Relevance of visco-plastic theory in a multi-directional inhomogeneous granular flow , 2009, 0904.4679.

[6]  A. Mainza,et al.  Characterising porosity of multi-component mixtures in rotary mills , 2011 .

[7]  D. Parker,et al.  The shape and behaviour of a granular bed in a rotating drum using Eulerian flow fields obtained from PEPT , 2016 .

[8]  Power-law friction in closely packed granular materials. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  J. Roux,et al.  Quasistatic rheology and the origins of strain , 2009, 0901.2846.

[10]  E R Dufresne,et al.  Minimal model for kinetic arrest. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  H. Rose,et al.  A treatise on the internal mechanics of ball, tube and rod mills , 1958 .

[12]  G. Midi,et al.  On dense granular flows , 2003, The European physical journal. E, Soft matter.

[13]  Olivier Pouliquen,et al.  Friction law for dense granular flows: application to the motion of a mass down a rough inclined plane , 2001, Journal of Fluid Mechanics.

[14]  S. Edwards,et al.  A model for the dynamics of sandpile surfaces , 1994 .

[15]  Marjolein Dijkstra,et al.  Pushing the glass transition towards random close packing using self-propelled hard spheres , 2013, Nature Communications.

[16]  Tamotsu Takahashi,et al.  A Review of Japanese Debris Flow Research , 2009 .

[17]  Testing of a new dynamic Ergun equation for transport with positron emission particle tracking , 2016 .

[18]  S. Savage,et al.  Analyses of slow high-concentration flows of granular materials , 1998, Journal of Fluid Mechanics.

[19]  J-P. Franzidis,et al.  Studies of the effect of tracer activity on time-averaged positron emission particle tracking measurements on tumbling mills at PEPT Cape Town , 2011 .

[20]  Granular pressure and the thickness of a layer jamming on a rough incline , 2005, cond-mat/0506155.

[21]  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.

[22]  Olivier Pouliquen,et al.  A constitutive law for dense granular flows , 2006, Nature.

[23]  John F. Canny,et al.  A Computational Approach to Edge Detection , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

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

[25]  Levine,et al.  Rotationally induced segregation of granular materials. , 1994, Physical review letters.

[26]  He Yurong,et al.  Numerical simulations of flow behavior of gas and particles in spouted beds using frictional-kinetic stresses model , 2009 .

[27]  A. V. Orpe,et al.  Rheology of surface granular flows , 2005, Journal of Fluid Mechanics.

[28]  I. Goldhirsch,et al.  RAPID GRANULAR FLOWS , 2003 .

[29]  Crucial role of sidewalls in granular surface flows: consequences for the rheology , 2005, Journal of Fluid Mechanics.

[30]  Parker,et al.  Single-particle motion in three-dimensional vibrofluidized granular beds , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[31]  J-P. Franzidis,et al.  Measurement of shear rates in a laboratory tumbling mill , 2011 .

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

[33]  Jean-Noël Roux,et al.  Rheophysics of dense granular materials: discrete simulation of plane shear flows. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  Jochen Mellmann,et al.  The transverse motion of solids in rotating cylinders—forms of motion and transition behavior , 2001 .

[35]  P. Gennes,et al.  Surface flows of granular materials: A modified picture for thick avalanches , 1998 .